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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

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1435-5337
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Volume 28, Issue 2

Issues

Topology of moduli spaces of free group representations in real reductive groups

Ana Casimiro / Carlos Florentino
  • Departamento Matemática, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
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/ Sean Lawton
  • Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, Virginia, 22030, USA
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/ André Oliveira
  • Departamento de Matemática, Universidade de Trás-os-Montes e Alto Douro, UTAD, Quinta dos Prados, 5001-801 Vila Real, Portugal
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Published Online: 2014-09-09 | DOI: https://doi.org/10.1515/forum-2014-0049

Abstract

Let G be a real reductive algebraic group with maximal compact subgroup K, and let Fr be a rank r free group. We show that the space of closed orbits in Hom(Fr,G)/G admits a strong deformation retraction to the orbit space Hom(Fr,K)/K. In particular, all such spaces have the same homotopy type. We compute the Poincaré polynomials of these spaces for some low rank groups G, such as Sp(4,ℝ) and U(2,2). We also compare these real moduli spaces to the real points of the corresponding complex moduli spaces, and describe the geometry of many examples.

Keywords: Character varieties; real reductive groups; representation varieties

MSC: 14D20; 32G13; 14L30; 14P25; 20E05

About the article

Received: 2014-03-21

Revised: 2014-07-02

Published Online: 2014-09-09

Published in Print: 2016-03-01


Funding Source: FCT, Portugal

Award identifier / Grant number: PTDC/MAT-GEO/0675/2012

Funding Source: FCT, Portugal

Award identifier / Grant number: PTDC/MAT/120411/2010

Funding Source: U.S. National Science Foundation

Award identifier / Grant number: DMS 1107452

Funding Source: U.S. National Science Foundation

Award identifier / Grant number: DMS 1107263

Funding Source: U.S. National Science Foundation

Award identifier / Grant number: DMS 1107367

Funding Source: Simons Foundation

Award identifier / Grant number: 245642

Funding Source: U.S. National Science Foundation

Award identifier / Grant number: DMS 1309376

Funding Source: Centro de Matemática da Universidade de Trás-os-Montes e Alto Douro

Award identifier / Grant number: PEst-OE/MAT/UI4080/2011


Citation Information: Forum Mathematicum, Volume 28, Issue 2, Pages 275–294, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2014-0049.

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