On the homotopy type of free group character varieties

Ana  Casimiro; Andre Oliveira; Carlos Florentino; Sean Lawton

On the homotopy type of free group character varieties

Ana Casimiro, Andre Oliveira, Carlos Florentino, Sean Lawton

DM - Departamento de Matemática

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

Abstract

Let G be a real reductive algebraic group with maximal compact subgroup K,
and let Fr be a rank r free group. Here, we summarize the construction of a natural strong deformation retraction from the space of closed orbits in Hom(Fr,G)/G to the orbit space Hom(Fr,K)/K. In particular, these spaces have the same homotopy type.

Original language	English
Number of pages	4
Journal	Boletim da Sociedade Portuguesa de Matemática
Publication status	Published - 2016

Keywords

Character varieties
Real reductive groups
Free group rep resentations

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title = "On the homotopy type of free group character varieties",

abstract = "Let G be a real reductive algebraic group with maximal compact subgroup K,and let Fr be a rank r free group. Here, we summarize the construction of a natural strong deformation retraction from the space of closed orbits in Hom(Fr,G)/G to the orbit space Hom(Fr,K)/K. In particular, these spaces have the same homotopy type.",

keywords = "Character varieties, Real reductive groups, Free group rep resentations",

author = "Ana Casimiro and Andre Oliveira and Carlos Florentino and Sean Lawton",

year = "2016",

language = "English",

journal = "Boletim da Sociedade Portuguesa de Matem{\'a}tica",

issn = "0872-3672",

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TY - JOUR

T1 - On the homotopy type of free group character varieties

AU - Casimiro, Ana

AU - Oliveira, Andre

AU - Florentino, Carlos

AU - Lawton, Sean

PY - 2016

Y1 - 2016

N2 - Let G be a real reductive algebraic group with maximal compact subgroup K,and let Fr be a rank r free group. Here, we summarize the construction of a natural strong deformation retraction from the space of closed orbits in Hom(Fr,G)/G to the orbit space Hom(Fr,K)/K. In particular, these spaces have the same homotopy type.

AB - Let G be a real reductive algebraic group with maximal compact subgroup K,and let Fr be a rank r free group. Here, we summarize the construction of a natural strong deformation retraction from the space of closed orbits in Hom(Fr,G)/G to the orbit space Hom(Fr,K)/K. In particular, these spaces have the same homotopy type.

KW - Character varieties

KW - Real reductive groups

KW - Free group rep resentations

UR - https://arxiv.org/pdf/1412.4396.pdf

M3 - Article

JO - Boletim da Sociedade Portuguesa de Matemática

JF - Boletim da Sociedade Portuguesa de Matemática

SN - 0872-3672

ER -

On the homotopy type of free group character varieties

Abstract

Keywords

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