Book Review
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MathSciNet review:
1568178
Full text of review:
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Book Information:
Author:
M. Schwarz
Title:
Morse homology
Additional book information:
Progress in Mathematics, vol. 111, Birkh\"auser Verlag, Basel and Boston, MA, 1993, ix+235 pp., US$49.50. ISBN 3-7643-\linebreak 2904-1.
Raoul Bott, Morse theory indomitable, Inst. Hautes Études Sci. Publ. Math. 68 (1988), 99–114 (1989). MR 1001450
Kung-ching Chang, Infinite-dimensional Morse theory and multiple solution problems, Progress in Nonlinear Differential Equations and their Applications, vol. 6, Birkhäuser Boston, Inc., Boston, MA, 1993. MR 1196690, DOI 10.1007/978-1-4612-0385-8
Charles Conley, Isolated invariant sets and the Morse index, CBMS Regional Conference Series in Mathematics, vol. 38, American Mathematical Society, Providence, R.I., 1978. MR 511133
C. C. Conley and E. Zehnder, The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnol′d, Invent. Math. 73 (1983), no. 1, 33–49. MR 707347, DOI 10.1007/BF01393824
Andreas Floer, A relative Morse index for the symplectic action, Comm. Pure Appl. Math. 41 (1988), no. 4, 393–407. MR 933228, DOI 10.1002/cpa.3160410402
Andreas Floer, Cuplength estimates on Lagrangian intersections, Comm. Pure Appl. Math. 42 (1989), no. 4, 335–356. MR 990135, DOI 10.1002/cpa.3160420402
Andreas Floer, An instanton-invariant for $3$-manifolds, Comm. Math. Phys. 118 (1988), no. 2, 215–240. MR 956166
Andreas Floer, Morse theory for Lagrangian intersections, J. Differential Geom. 28 (1988), no. 3, 513–547. MR 965228
Andreas Floer, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), no. 4, 575–611. MR 987770
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, Witten’s complex and infinite-dimensional Morse theory, J. Differential Geom. 30 (1989), no. 1, 207–221. MR 1001276
John M. Franks, Morse-Smale flows and homotopy theory, Topology 18 (1979), no. 3, 199–215. MR 546790, DOI 10.1016/0040-9383(79)90003-X
M. Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), no. 2, 307–347. MR 809718, DOI 10.1007/BF01388806
John Milnor, Lectures on the $h$-cobordism theorem, Princeton University Press, Princeton, N.J., 1965. Notes by L. Siebenmann and J. Sondow. MR 0190942
[15] -, Morse theory, Ann. of Math. Stud., vol. 51, Princeton Univ. Press, Princeton, NJ, 1963.
S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
Stephen Smale, On gradient dynamical systems, Ann. of Math. (2) 74 (1961), 199–206. MR 133139, DOI 10.2307/1970311
René Thom, Sur une partition en cellules associée à une fonction sur une variété, C. R. Acad. Sci. Paris 228 (1949), 973–975 (French). MR 29160
Edward Witten, Supersymmetry and Morse theory, J. Differential Geometry 17 (1982), no. 4, 661–692 (1983). MR 683171
- [1]
- R. Bott, Morse theory indomitable, Publ. Math. Inst. Hautes Études Sci. (1988), 99-114. MR 1001450 (90f:58027)
- [2]
- K.-C. Chang, Infinite dimensional Morse theory and multiple solution problems, Birkhäuser, Basel and Boston, MA, 1993. MR 1196690 (94e:58023)
- [3]
- C. Conley, Isolated invariant sets and Morse index, CBMS Regional Conf. Ser. in Math., vol. 38, Amer. Math. Soc., Providence, RI, 1978. MR 511133 (80c:58009)
- [4]
- C. Conley and E. Zehnder, The Birkhoff-Lewis fixed point theorem and a conjecture of V. I. Arnold, Invent. Math. 73 (1983), 33-49. MR 707347 (85e:58044)
- [5]
- A. Floer, A relative index for the symplectic action, Comm. Pure Appl. Math. 41 (1988), 393-407. MR 933228 (89f:58055)
- [6]
- -, Cuplength estimates on Lagrangian intersections, Comm. Pure Appl. Math. 42 (1989), 335-356. MR 990135 (90g:58034)
- [7]
- -, An instanton invariant for 3-manifolds, Comm. Math. Phys. 118 (1988), 215-240. MR 956166 (89k:57028)
- [8]
- -, Morse theory for Lagrangian intersection theory, J. Differential Geom. 18 (1988), 513-517. MR 965228 (90f:58058)
- [9]
- -, Symplectic fixed points and holomorphic spheres, Comm. Math. Phys. 120 (1989), 576-611. MR 987770 (90e:58047)
- [10]
- -, The unregularised gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988), 775-813. MR 948771 (89g:58065)
- [11]
- -, Witten's complex and infinite dimensional Morse theory, J. Differential Geom. 30 (1989), 207-221. MR 1001276 (90d:58029)
- [12]
- J. Franks, Morse-Smale flows and homotopy theory, Topology 18 (1979), 199-215. MR 546790 (80k:58063)
- [13]
- M. Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985), 307-347. MR 809718 (87j:53053)
- [14]
- J. Milnor, Lectures on the h-cobordism theorem, Princeton Univ. Press, Princeton, NJ, 1965. MR 0190942 (32:8352)
- [15]
- -, Morse theory, Ann. of Math. Stud., vol. 51, Princeton Univ. Press, Princeton, NJ, 1963.
- [16]
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 0228014 (37:3598)
- [17]
- -, On gradient dynamical systems, Ann. of Math. 74 (1961), 199-206. MR 0133139 (24:A2973)
- [18]
- R. Thom, Sur une partition en cellules associés à une fonction sur une variété, C. R. Acad. Sci. Paris Sér. I Math. 228 (1949), 973-975. MR 0029160 (10:558b)
- [19]
- E. Witten, Supersymmetry and Morse theory, J. Differential Geom. 17 (1982), 661-692. MR 683171 (84b:58111)
Review Information:
Reviewer:
Helmut Hofer
Journal:
Bull. Amer. Math. Soc.
32 (1995), 330-334
DOI:
https://doi.org/10.1090/S0273-0979-1995-00591-4
