A note on Reidemeister Torsion of G-Anosov Representations

2021/01/20 by Zeybek, Hatice, Sozen, Yasar
#32G15 #57R30 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2101.08066

Abstract

This article considers G-Anosov representations of a fixed closed oriented Riemann surface Σ of genus at least 2. Here, G is the Lie group PSp(2n,ℝ), PSO(n,n) or PSO(n,n+1). It proves that Reidemeister torsion (R-torsion) associated to Σ with coefficients in the adjoint bundle representations of such representations is well-defined. Moreover, by using symplectic chain complex method, it establishes a novel formula for R-torsion of such representations in terms of the Atiyah-Bott-Goldman symplectic form corresponding to the Lie group G. Furtermore, it applies the results to Hitchin components, in particular, Teichmüller space.

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