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Problems on Mapping Class Groups and Related Topics

About this Title

Benson Farb, University of Chicago, Chicago, IL, Editor

Publication: Proceedings of Symposia in Pure Mathematics
Publication Year: 2006; Volume 74
ISBNs: 978-0-8218-3838-9 (print); 978-0-8218-9380-7 (online)
DOI: https://doi.org/10.1090/pspum/074

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Table of Contents

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Front/Back Matter

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I. Cohomological, combinatorial and algebraic structures

• Mladen Bestvina – Four questions about mapping class groups [MR 2264129]
• Benson Farb – Some problems on mapping class groups and moduli space [MR 2264130]
• Richard Hain – Finiteness and Torelli spaces [MR 2264131]
• Nikolai V. Ivanov – Fifteen problems about the mapping class groups [MR 2264532]
• Mustafa Korkmaz – Problems on homomorphisms of mapping class groups [MR 2264533]
• Ib Madsen – The mapping class group and homotopy theory [MR 2264534]
• R. C. Penner – Probing mapping class groups using arcs [MR 2264535]
• Bronislaw Wajnryb – Relations in the mapping class group [MR 2264536]

II. Connections with 3-manifolds, symplectic geometry and algebraic geometry

• Denis Auroux – Mapping class group factorizations and symplectic 4-manifolds: some open problems [MR 2264537]
• Joan S. Birman – The topology of 3-manifolds, Heegaard distance and the mapping class group of a 2-manifold [MR 2264538]
• S. K. Donaldson – Lefschetz pencils and mapping class groups [MR 2264539]
• Pierre Lochak and Leila Schneps – Open problems in Grothendieck-Teichmüller theory [MR 2264540]

III. Geometric and dynamical aspects

• William M. Goldman – Mapping class group dynamics on surface group representations [MR 2264541]
• Ursula Hamenstädt – Geometric properties of the mapping class group [MR 2264542]
• Pascal Hubert, Howard Masur, Thomas Schmidt and Anton Zorich – Problems on billiards, flat surfaces and translation surfaces [MR 2264543]
• Lee Mosher – Problems in the geometry of surface group extensions [MR 2264544]
• Alan W. Reid – Surface subgroups of mapping class groups [MR 2264545]
• Scott A. Wolpert – Weil-Petersson perspectives [MR 2264546]

IV. Braid groups, $\mathrm {Out}(F_n)$ and other related groups

• Stephen Bigelow – Braid groups and Iwahori-Hecke algebras [MR 2264547]
• Martin R. Bridson and Karen Vogtmann – Automorphism groups of free groups, surface groups and free abelian groups [MR 2264548]
• F. R. Cohen – Problems: Braid groups, homotopy, cohomology, and representations [MR 2264549]
• Shigeyuki Morita – Cohomological structure of the mapping class group and beyond [MR 2264550]
• Luis Paris – From braid groups to mapping class groups [MR 2264551]