The mapping class group of a genus two surface is linear

DOI10.2140/agt.2001.1.699zbMath0999.57020arXivmath/0010310OpenAlexW1973249989MaRDI QIDQ5949337

Stephen J. Bigelow, Ryan D. Budney

Publication date: 10 December 2001

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0010310

zbMATH Keywords

representationmapping class grouplinearbraid group

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) General low-dimensional topology (57M99) Braid groups; Artin groups (20F36) Topological methods in group theory (57M07) Other groups related to topology or analysis (20F38)

Related Items (21)

Frattini and related subgroups of mapping class groups ⋮ The hyperelliptic mapping class group of a nonorientable surface of genus \(g\geq 4\) has a faithful representation into \(\operatorname{GL}(g^2 - 1, \mathbb{R})\) ⋮ Linear representations of the braid groups of some manifolds. ⋮ Low‐dimensional linear representations of mapping class groups ⋮ Weakly framed surface configurations, Heisenberg homology, and mapping class group action ⋮ Hierarchically hyperbolic groups and uniform exponential growth ⋮ ON AUTOMORPHISMS OF SURFACE BRAID GROUPS ⋮ ABELIAN AND METABELIAN QUOTIENT GROUPS OF SURFACE BRAID GROUPS ⋮ Quantum \(SU(2)\) faithfully detects mapping class groups modulo center ⋮ Asymptotic linearity of the mapping class group and a homological version of the Nielsen-Thurston classification ⋮ Aspects of non positive curvature for linear groups with no infinite order unipotents ⋮ ON THE IMAGE OF THE LAWRENCE–KRAMMER REPRESENTATION ⋮ Mapping class groups of covers with boundary and braid group embeddings ⋮ On the kernel of the Magnus representation of the Torelli group ⋮ On the linearity problem for mapping class groups ⋮ An effective Lie-Kolchin theorem for quasi-unipotent matrices ⋮ Asymptotic mapping class groups of closed surfaces punctured along Cantor sets ⋮ Congruence subgroups of braid groups ⋮ Braid groups and mapping class groups: The Birman–Hilden theory ⋮ A finite presentation for the hyperelliptic mapping class group of a nonorientable surface ⋮ On visualization of the linearity problem for mapping class groups of surfaces

Cites Work

• On isotopies of homeomorphisms of Riemann surfaces
• Differential Topology
• Braid groups are linear
• The Nielsen realization problem
• Braid groups are linear
• The braid group \(B_4\) is linear
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