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Complex Geometry of Groups
Edited by: Angel Carocca, Pontificia Universidad Católica de Chile, Santiago, Chile, Víctor González-Aguilera, Universidad Técnica Federico Santa María, Valparaíso, Chile, and Rubí E. Rodríguez, Pontificia Universidad Católica de Chile, Santiago
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Contemporary Mathematics
1999; 286 pp; softcover
Volume: 240
ISBN-10: 0-8218-1381-1
ISBN-13: 978-0-8218-1381-2
List Price: US$80 Member Price: US$64
Order Code: CONM/240

This volume presents the proceedings of the I Iberoamerican Congress on Geometry: Cruz del Sur held in Olmué, Chile. The main topic was "The Geometry of Groups: Curves, Abelian Varieties, Theoretical and Computational Aspects". Participants came from all over the world.

The volume gathers the expanded contributions from most of the participants in the Congress. Articles reflect the topic in its diversity and unity, and in particular, the work done on the subject by Iberoamerican mathematicians. Original results and surveys are included on the following areas: curves and Riemann surfaces, abelian varieties, and complex dynamics. The approaches are varied, including Kleinian groups, quasiconformal mappings and Teichmüller spaces, function theory, moduli spaces, automorphism groups, algebraic geometry, and more.

Graduate students and research mathematicians interested in functions of a complex variable.

• R. E. Rodríguez -- Complex geometry in Chile: Panorama and perspectives
• W. Abikoff -- Quasiconformal conjugation of Möbius transformations
• R. Bamón -- A family of n-dimensional differential equations with Lorenz-like attractors
• C. Birkenhake, H. Lange, and V. González-Aguilera -- Automorphisms of $$3$$-dimensional abelian varieties
• L. Brambila-Paz, L. Hidalgo-Solís, and J. Muciño-Raymundo -- On restrictions of the Picard bundle
• A. M. Castro -- Representations of triangle groups in the Heisenberg group
• M. Chuaqui and B. Osgood -- Recent progress on the geometry of univalence criteria
• A. F. Costa and A. M. Porto -- On anticonformal automorphisms of order $$>2$$ of Riemann
• C. J. Earle, F. P. Gardiner, and N. Lakic -- Isomorphisms between generalized Teichmüller spaces
• H. M. Farkas and I. Kra -- Ramanujan partition identities
• H. M. Farkas and I. Kra -- A function theoretic approach to the Ramanujan partition identities with applications to combinatorial number theory
• F. Gardiner and L. Keen -- Holomorphic motions and quasifuchsian manifolds
• L. Giraldo, X. Gómez-Mont, and P. Mardešić -- Computation of topological numbers via linear algebra: hypersurfaces, vector fields and vector fields on hypersurfaces
• E. Gómez González -- Cyclic coverings of a smooth curve and branch locus of the moduli space of smooth curves
• G. González-Díez and W. J. Harvey -- Subvarieties of moduli space for Riemann surfaces
• R. A. Hidalgo -- Noded function groups
• L. Hidalgo-Solís and S. Recillas-Pishmish -- The hyperelliptic fibre of the Prym map in genus four
• J. Kiwi -- From the shift loci to the connectedness loci of complex polynomials
• Y. A. Kopylov -- Some properties of the operator of exterior derivation on surfaces of revolution and $$\mathbb{L_p}$$-cohomology
• B. Maskit -- Matrices for Fenchel-Nielsen parameters in genus $$2$$
• T. Nakanishi, M. Näätänen, and G. Rosenberger -- Arithmetic Fuchsian groups of signature $$(0;e_1,e_2,e_3,e_4)$$ with $$2 \leq e_1 \leq e_2 \leq e_3$$, $$e_4 = \infty$$
• J. R. Quine -- Geometric and holomorphic moduli for extremal Riemann surfaces