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

Ana Casimiro, Carlos Florentino, Sean Lawton, André Oliveira

Research output: Contribution to journalArticle

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Abstract

Let G be a real reductive algebraic group with maximal compact subgroup K, and let F-r be a rank r free group. We show that the space of closed orbits in Hom(F-r, G)/G admits a strong deformation retraction to the orbit space Hom(F-r, K)/K. In particular, all such spaces have the same homotopy type. We compute the Poincare polynomials of these spaces for some low rank groups G, such as Sp(4, IR) 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.

Original languageEnglish
Pages (from-to)275-294
Number of pages20
JournalForum mathematicum
Volume28
Issue number2
DOIs
Publication statusPublished - Mar 2016

Keywords

  • Character varieties
  • real reductive groups
  • representation varieties
  • CHARACTER VARIETIES
  • 2X2 MATRICES
  • 3-MANIFOLDS
  • INVARIANTS
  • SPLITTINGS
  • SURFACE

Cite this

Casimiro, Ana ; Florentino, Carlos ; Lawton, Sean ; Oliveira, André. / Topology of moduli spaces of free group representations in real reductive groups. In: Forum mathematicum. 2016 ; Vol. 28, No. 2. pp. 275-294.
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note = "This work was partially supported by the projects PTDC/MAT-GEO/0675/2012 and PTDC/MAT/120411/2010, FCT, Portugal. The authors also acknowledge support from U.S. National Science Foundation grants DMS 1107452, 1107263, 1107367 {"}RNMS: Geometric structures and Representation varieties{"} (the GEAR Network). Additionally, the third author was partially supported by the Simons Foundation grant 245642 and the U.S. National Science Foundation grant DMS 1309376, and the fourth author was partially supported by Centro de Matematica da Universidade de Tras-os-Montes e Alto Douro (PEst-OE/MAT/UI4080/2011).",
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Topology of moduli spaces of free group representations in real reductive groups. / Casimiro, Ana; Florentino, Carlos; Lawton, Sean; Oliveira, André.

In: Forum mathematicum, Vol. 28, No. 2, 03.2016, p. 275-294.

Research output: Contribution to journalArticle

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