Borel class and Cartan involution

2017/11/20 by Thilo Kuessner, Kuessner, Thilo
Mathematics · #57M50 #Advanced Operator Algebra Research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1711.07443

openalex publication_date 2017/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove that the Borel class of representations of 3-manifold groups to PGL(n,C) is preserved under Cartan involution up to sign. For representations to PGL(3,C) this is implied by a more general result of E. Falbel and Q. Wang, however our proof appears to be much shorter for that special case.

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