\renewcommand{\bibname}References

• Mohammed Abouzaid, On the Fukaya categories of higher genus surfaces, Adv. Math. 217 (2008), no. 3, 1192–1235. MR 2383898, DOI 10.1016/j.aim.2007.08.011
• Mohammed Abouzaid, Denis Auroux, Alexander I. Efimov, Ludmil Katzarkov, and Dmitri Orlov, Homological mirror symmetry for punctured spheres, J. Amer. Math. Soc. 26 (2013), no. 4, 1051–1083. MR 3073884, DOI 10.1090/S0894-0347-2013-00770-5
• Lars V. Ahlfors, Complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1978. An introduction to the theory of analytic functions of one complex variable; International Series in Pure and Applied Mathematics. MR 510197
• Samuel J. Blank, Extending immersions of the circle, Dissertation, Brandise University, Waltham, Mass., 1967. (Cited on page \pageref{FRANCIS2,TITUS,BLANK,POENARU}.)
• Paul Biran and Octav Cornea, A Lagrangian quantum homology, New perspectives and challenges in symplectic field theory, CRM Proc. Lecture Notes, vol. 49, Amer. Math. Soc., Providence, RI, 2009, pp. 1–44. MR 2555932, DOI 10.1090/crmp/049/01
• Vin De Silva, Products in the symplectic Floer homology of Lagrangian intersections, PhD thesis, Oxford, 1999. (Cited on pages \pageref{DESILVA0}, \pageref{DESILVA1}, \pageref{DESILVA2}.)
• Clifford J. Earle and James Eells, A fibre bundle description of Teichmüller theory, J. Differential Geometry 3 (1969), 19–43. MR 276999
• D. B. A. Epstein, Curves on $2$-manifolds and isotopies, Acta Math. 115 (1966), 83–107. MR 214087, DOI 10.1007/BF02392203
• David Epstein, private communication, 6 April 2000. (Cited on pages \pageref{DBAE1}, \pageref{DBAE2}.)
• Andreas Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988), no. 6, 775–813. MR 948771, DOI 10.1002/cpa.3160410603
• Andreas Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988), no. 3, 513–547. MR 965228
• George K. Francis, Spherical curves that bound immersed discs, Proc. Amer. Math. Soc. 41 (1973), 87–93. MR 321112, DOI 10.1090/S0002-9939-1973-0321112-0
• Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono, Lagrangian Intersection Floer Theory: Anomaly and Obstruction. AMS/IP Studies in Advanced Mathematics, vol. 46, American Mathematical Society, Providence, RI, 2009. MR2310372 (2008d:53033) (Cited on page \pageref{FOOO1}, \pageref{FOOO2}.)
• Ralf Gautschi, Joel W. Robbin, and Dietmar A. Salamon, Heegaard splittings and Morse-Smale flows, Int. J. Math. Math. Sci. 56 (2003), 3539–3572. MR 2020083, DOI 10.1155/S0161171203210115
• Michael Hutchings and Yi-Jen Lee, Circle-valued Morse theory and Reidemeister torsion, Geom. Topol. 3 (1999), 369–396. MR 1716272, DOI 10.2140/gt.1999.3.369
• Michael Hutchings and Yi-Jen Lee, Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of $3$-manifolds, Topology 38 (1999), no. 4, 861–888. MR 1679802, DOI 10.1016/S0040-9383(98)00044-5
• Michael Khanevsky, Hofer’s metric on the space of diameters, J. Topol. Anal. 1 (2009), no. 4, 407–416. MR 2597651, DOI 10.1142/S1793525309000187
• Maxim Kontsevich, Homological algebra of mirror symmetry, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994) Birkhäuser, Basel, 1995, pp. 120–139. MR 1403918
• John W. Milnor, Topology from the differentiable viewpoint, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Based on notes by David W. Weaver; Revised reprint of the 1965 original. MR 1487640
• Dusa McDuff and Dietmar Salamon, $J$-holomorphic curves and symplectic topology, American Mathematical Society Colloquium Publications, vol. 52, American Mathematical Society, Providence, RI, 2004. MR 2045629
• Yong-Geun Oh, Floer cohomology of Lagrangian intersections and pseudoholomorphic discs I, II. Comm Pure Appl. Math., 46 (1993), 949–94, 995–1012. III. Arnold–Givental conjecture. In The Floer Memorial Volume, edited by Hofer, Taubes, Weinstein, and Zehnder, Birkhäuser, Basel, 1995, pp. 555–574. (Cited on pages \pageref{OHa}, \pageref{OHb}.)
• A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz numbers, and matrix models, Algebraic geometry—Seattle 2005. Part 1, Proc. Sympos. Pure Math., vol. 80, Amer. Math. Soc., Providence, RI, 2009, pp. 325–414. MR 2483941, DOI 10.1090/pspum/080.1/2483941
• A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. (2) 163 (2006), no. 2, 517–560. MR 2199225, DOI 10.4007/annals.2006.163.517
• A. Okounkov and R. Pandharipande, The equivariant Gromov-Witten theory of $\textbf {P}^1$, Ann. of Math. (2) 163 (2006), no. 2, 561–605. MR 2199226, DOI 10.4007/annals.2006.163.561
• A. Okounkov and R. Pandharipande, Virasoro constraints for target curves, Invent. Math. 163 (2006), no. 1, 47–108. MR 2208418, DOI 10.1007/s00222-005-0455-y
• Peter Ozsváth and Zoltán Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (2004), no. 3, 1027–1158. MR 2113019, DOI 10.4007/annals.2004.159.1027
• Peter Ozsváth and Zoltán Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. (2) 159 (2004), no. 3, 1159–1245. MR 2113020, DOI 10.4007/annals.2004.159.1159
• Valentin Poenaru, Extensions des immersions en codimension 1 (d’apres Samuel Blank), Sem. Bourbaki, 1967/68, Exposé 342. (Cited on page \pageref{FRANCIS2,TITUS,BLANK,POENARU}.)
• Marcin Pozniak, Floer homology, Novikov rings, and clean intersections, PhD thesis, University of Warwick, 1994. (Cited on page \pageref{POZNIAK}.)
• Joel Robbin and Dietmar Salamon, The Maslov index for paths, Topology 32 (1993), no. 4, 827–844. MR 1241874, DOI 10.1016/0040-9383(93)90052-W
• Joel Robbin and Dietmar Salamon, The spectral flow and the Maslov index, Bull. London Math. Soc. 27 (1995), no. 1, 1–33. MR 1331677, DOI 10.1112/blms/27.1.1
• Joel W. Robbin and Dietmar A. Salamon, Asymptotic behaviour of holomorphic strips, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001), no. 5, 573–612 (English, with English and French summaries). MR 1849689, DOI 10.1016/S0294-1449(00)00066-4
• Paul Seidel, Graded Lagrangian submanifolds, Bull. Soc. Math. France 128 (2000), no. 1, 103–149 (English, with English and French summaries). MR 1765826
• Paul Seidel, Fukaya categories and Picard-Lefschetz theory, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich, 2008. MR 2441780
• Paul Seidel, Homological mirror symmetry for the genus two curve, J. Algebraic Geom. 20 (2011), no. 4, 727–769. MR 2819674, DOI 10.1090/S1056-3911-10-00550-3
• Tatjana Simcevic, A Hardy space approach to Floer gluing. PhD thesis, ETH Zürich, in preparation. (Cited on page \pageref{SIMCEVIC}.)
• Stephen Smale, Diffeomorphisms of the $2$-sphere, Proc. Amer. Math. Soc. 10 (1959), 621–626. MR 112149, DOI 10.1090/S0002-9939-1959-0112149-8
• Charles J. Titus, The combinatorial topology of analytic functions on the boundary of a disk, Acta Math. 106 (1961), 45–64. MR 166375, DOI 10.1007/BF02545813
• Claude Viterbo, Intersection de sous-variétés lagrangiennes, fonctionnelles d’action et indice des systèmes hamiltoniens, Bull. Soc. Math. France 115 (1987), no. 3, 361–390 (French, with English summary). MR 926533

\renewcommand{\bibname}References

• Mohammed Abouzaid, On the Fukaya categories of higher genus surfaces, Adv. Math. 217 (2008), no. 3, 1192–1235. MR 2383898 (2008k:53198), DOI 10.1016/j.aim.2007.08.011
• Mohammed Abouzaid, Denis Auroux, Alexander I. Efimov, Ludmil Katzarkov, and Dmitri Orlov, Homological mirror symmetry for punctured spheres, J. Amer. Math. Soc. 26 (2013), no. 4, 1051–1083. MR 3073884, DOI 10.1090/S0894-0347-2013-00770-5
• Lars V. Ahlfors, Complex analysis, 3rd ed., McGraw-Hill Book Co., New York, 1978. An introduction to the theory of analytic functions of one complex variable; International Series in Pure and Applied Mathematics. MR 510197 (80c:30001)
• Samuel J. Blank, Extending immersions of the circle, Dissertation, Brandise University, Waltham, Mass., 1967. (Cited on page \pageref{FRANCIS2,TITUS,BLANK,POENARU}.)
• Paul Biran and Octav Cornea, A Lagrangian quantum homology, New perspectives and challenges in symplectic field theory, CRM Proc. Lecture Notes, vol. 49, Amer. Math. Soc., Providence, RI, 2009, pp. 1–44. MR 2555932 (2010m:53132)
• Vin De Silva, Products in the symplectic Floer homology of Lagrangian intersections, PhD thesis, Oxford, 1999. (Cited on pages \pageref{DESILVA0}, \pageref{DESILVA1}, \pageref{DESILVA2}.)
• Clifford J. Earle and James Eells, A fibre bundle description of Teichmüller theory, J. Differential Geometry 3 (1969), 19–43. MR 0276999 (43 \#2737a)
• D. B. A. Epstein, Curves on $2$-manifolds and isotopies, Acta Math. 115 (1966), 83–107. MR 0214087 (35 \#4938)
• David Epstein, private communication, 6 April 2000. (Cited on pages \pageref{DBAE1}, \pageref{DBAE2}.)
• Andreas Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988), no. 6, 775–813. MR 948771 (89g:58065), DOI 10.1002/cpa.3160410603
• Andreas Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988), no. 3, 513–547. MR 965228 (90f:58058)
• George K. Francis, Spherical curves that bound immersed discs, Proc. Amer. Math. Soc. 41 (1973), 87–93. MR 0321112 (47 \#9645)
• Kenji Fukaya, Yong-Geun Oh, Hiroshi Ohta, Kaoru Ono, Lagrangian Intersection Floer Theory: Anomaly and Obstruction. AMS/IP Studies in Advanced Mathematics, vol. 46, American Mathematical Society, Providence, RI, 2009. MR2310372 (2008d:53033) (Cited on page \pageref{FOOO1}, \pageref{FOOO2}.)
• Ralf Gautschi, Joel W. Robbin, and Dietmar A. Salamon, Heegaard splittings and Morse-Smale flows, Int. J. Math. Math. Sci. 56 (2003), 3539–3572. MR 2020083 (2004m:57065), DOI 10.1155/S0161171203210115
• Michael Hutchings and Yi-Jen Lee, Circle-valued Morse theory and Reidemeister torsion, Geom. Topol. 3 (1999), 369–396. MR 1716272 (2000h:57063), DOI 10.2140/gt.1999.3.369
• Michael Hutchings and Yi-Jen Lee, Circle-valued Morse theory, Reidemeister torsion, and Seiberg-Witten invariants of $3$-manifolds, Topology 38 (1999), no. 4, 861–888. MR 1679802 (2000i:57055), DOI 10.1016/S0040-9383(98)00044-5
• Michael Khanevsky, Hofer’s metric on the space of diameters, J. Topol. Anal. 1 (2009), no. 4, 407–416. MR 2597651 (2011c:53195), DOI 10.1142/S1793525309000187
• Maxim Kontsevich, Homological algebra of mirror symmetry, 2 (Zürich, 1994) Birkhäuser, Basel, 1995, pp. 120–139. MR 1403918 (97f:32040)
• John W. Milnor, Topology from the differentiable viewpoint, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Based on notes by David W. Weaver; Revised reprint of the 1965 original. MR 1487640 (98h:57051)
• Dusa McDuff and Dietmar Salamon, $J$-holomorphic curves and symplectic topology, American Mathematical Society Colloquium Publications, vol. 52, American Mathematical Society, Providence, RI, 2004. MR 2045629 (2004m:53154)
• Yong-Geun Oh, Floer cohomology of Lagrangian intersections and pseudoholomorphic discs I, II. Comm Pure Appl. Math., 46 (1993), 949–94, 995–1012. III. Arnold–Givental conjecture. In The Floer Memorial Volume, edited by Hofer, Taubes, Weinstein, and Zehnder, Birkhäuser, Basel, 1995, pp. 555–574. (Cited on pages \pageref{OHa}, \pageref{OHb}.)
• A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz numbers, and matrix models, Algebraic geometry—Seattle 2005. Part 1, Proc. Sympos. Pure Math., vol. 80, Amer. Math. Soc., Providence, RI, 2009, pp. 325–414. MR 2483941 (2009k:14111)
• A. Okounkov and R. Pandharipande, Gromov-Witten theory, Hurwitz theory, and completed cycles, Ann. of Math. (2) 163 (2006), no. 2, 517–560. MR 2199225 (2007b:14123), DOI 10.4007/annals.2006.163.517
• A. Okounkov and R. Pandharipande, The equivariant Gromov-Witten theory of $\textbf {P}^1$, Ann. of Math. (2) 163 (2006), no. 2, 561–605. MR 2199226 (2006j:14075), DOI 10.4007/annals.2006.163.561
• A. Okounkov and R. Pandharipande, Virasoro constraints for target curves, Invent. Math. 163 (2006), no. 1, 47–108. MR 2208418 (2006m:14077), DOI 10.1007/s00222-005-0455-y
• Peter Ozsváth and Zoltán Szabó, Holomorphic disks and topological invariants for closed three-manifolds, Ann. of Math. (2) 159 (2004), no. 3, 1027–1158. MR 2113019 (2006b:57016), DOI 10.4007/annals.2004.159.1027
• Peter Ozsváth and Zoltán Szabó, Holomorphic disks and three-manifold invariants: properties and applications, Ann. of Math. (2) 159 (2004), no. 3, 1159–1245. MR 2113020 (2006b:57017), DOI 10.4007/annals.2004.159.1159
• Valentin Poenaru, Extensions des immersions en codimension 1 (d’apres Samuel Blank), Sem. Bourbaki, 1967/68, Exposé 342. (Cited on page \pageref{FRANCIS2,TITUS,BLANK,POENARU}.)
• Marcin Pozniak, Floer homology, Novikov rings, and clean intersections, PhD thesis, University of Warwick, 1994. (Cited on page \pageref{POZNIAK}.)
• Joel Robbin and Dietmar Salamon, The Maslov index for paths, Topology 32 (1993), no. 4, 827–844. MR 1241874 (94i:58071), DOI 10.1016/0040-9383(93)90052-W
• Joel Robbin and Dietmar Salamon, The spectral flow and the Maslov index, Bull. London Math. Soc. 27 (1995), no. 1, 1–33. MR 1331677 (96d:58021), DOI 10.1112/blms/27.1.1
• Joel W. Robbin and Dietmar A. Salamon, Asymptotic behaviour of holomorphic strips, Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (2001), no. 5, 573–612 (English, with English and French summaries). MR 1849689 (2002e:53135), DOI 10.1016/S0294-1449(00)00066-4
• Paul Seidel, Graded Lagrangian submanifolds, Bull. Soc. Math. France 128 (2000), no. 1, 103–149 (English, with English and French summaries). MR 1765826 (2001c:53114)
• Paul Seidel, Fukaya categories and Picard-Lefschetz theory, Zurich Lectures in Advanced Mathematics, European Mathematical Society (EMS), Zürich, 2008. MR 2441780 (2009f:53143)
• Paul Seidel, Homological mirror symmetry for the genus two curve, J. Algebraic Geom. 20 (2011), no. 4, 727–769. MR 2819674 (2012f:53186), DOI 10.1090/S1056-3911-10-00550-3
• Tatjana Simcevic, A Hardy space approach to Floer gluing. PhD thesis, ETH Zürich, in preparation. (Cited on page \pageref{SIMCEVIC}.)
• Stephen Smale, Diffeomorphisms of the $2$-sphere, Proc. Amer. Math. Soc. 10 (1959), 621–626. MR 0112149 (22 \#3004)
• Charles J. Titus, The combinatorial topology of analytic functions on the boundary of a disk, Acta Math. 106 (1961), 45–64. MR 0166375 (29 \#3652)
• Claude Viterbo, Intersection de sous-variétés lagrangiennes, fonctionnelles d’action et indice des systèmes hamiltoniens, Bull. Soc. Math. France 115 (1987), no. 3, 361–390 (French, with English summary). MR 926533 (89b:58081)