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

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Casimiro, A (Author) Other; Florentino, C (Author) Other; Lawton, S (Author) Other; Oliveira, A (Author) FCUP

Journal

Title: Forum Mathematicum

Vol. 28

Pages: 275-294

ISSN: 0933-7741

Publisher: Walter De Gruyter

Indexing

ISI Web of Knowledge - 7 Citations

Scopus - 7 Citations

Other information

Authenticus ID: P-00K-8W2

DOI: 10.1515/forum-2014-0049

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20