The action of the Torelli group on the homology of representation spaces is nontrivial *

S. E. Cappell; R. Lee; E. Y. Miller

doi:10.1016/S0040-9383(99)00044-0

The action of the Torelli group on the homology of representation spaces is nontrivial *

S. E. Cappell, R. Lee, E. Y. Miller

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The mapping class group and its subgroup, the Torelli group, of a Riemann surface M has a natural action on the space R_SU(2)(M) of SU(2)-representations of the fundamental group of M and its subspace R_SU(2)(M))_irred of irreducibles. In this paper we compute the cohomology H* (R_SU(2)(M)), H* (R_SU(2)M(M)_irred) of both of these spaces and show that the induced action of the Torelli group is non-trivial.

Original language	English (US)
Pages (from-to)	851-871
Number of pages	21
Journal	Topology
Volume	39
Issue number	4
DOIs	https://doi.org/10.1016/S0040-9383(99)00044-0
State	Published - Jul 2000

Keywords

Gauge theory
Mapping class group
Moduli space
Representation variety
Torelli group

ASJC Scopus subject areas

Geometry and Topology

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10.1016/S0040-9383(99)00044-0

Cite this

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title = "The action of the Torelli group on the homology of representation spaces is nontrivial *",

abstract = "The mapping class group and its subgroup, the Torelli group, of a Riemann surface M has a natural action on the space RSU(2)(M) of SU(2)-representations of the fundamental group of M and its subspace RSU(2)(M))irred of irreducibles. In this paper we compute the cohomology H* (RSU(2)(M)), H* (RSU(2)M(M)irred) of both of these spaces and show that the induced action of the Torelli group is non-trivial.",

keywords = "Gauge theory, Mapping class group, Moduli space, Representation variety, Torelli group",

author = "Cappell, {S. E.} and R. Lee and Miller, {E. Y.}",

note = "Funding Information: * Corresponding author. E-mail address: rlee@math.yale.edu (R. Lee) ☆During the research of this paper, all three authors were supported by grants from the National Science Foundation.",

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T1 - The action of the Torelli group on the homology of representation spaces is nontrivial *

AU - Cappell, S. E.

AU - Lee, R.

AU - Miller, E. Y.

N1 - Funding Information: * Corresponding author. E-mail address: rlee@math.yale.edu (R. Lee) ☆During the research of this paper, all three authors were supported by grants from the National Science Foundation.

PY - 2000/7

Y1 - 2000/7

N2 - The mapping class group and its subgroup, the Torelli group, of a Riemann surface M has a natural action on the space RSU(2)(M) of SU(2)-representations of the fundamental group of M and its subspace RSU(2)(M))irred of irreducibles. In this paper we compute the cohomology H* (RSU(2)(M)), H* (RSU(2)M(M)irred) of both of these spaces and show that the induced action of the Torelli group is non-trivial.

AB - The mapping class group and its subgroup, the Torelli group, of a Riemann surface M has a natural action on the space RSU(2)(M) of SU(2)-representations of the fundamental group of M and its subspace RSU(2)(M))irred of irreducibles. In this paper we compute the cohomology H* (RSU(2)(M)), H* (RSU(2)M(M)irred) of both of these spaces and show that the induced action of the Torelli group is non-trivial.

KW - Gauge theory

KW - Mapping class group

KW - Moduli space

KW - Representation variety

KW - Torelli group

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EP - 871

JO - Topology

JF - Topology

IS - 4

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The action of the Torelli group on the homology of representation spaces is nontrivial *

Abstract

Keywords

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