2022/02/13 by Инканг Ким, Pierre Pansu, Kim, Inkang +3
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Representation Theory (math.RT) #Spectral Theory (math.SP)
paper · pdf · doi:10.48550/arxiv.2202.06436
openalex publication_date 2022/02/13 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
This paper deals with the representations of the fundamental groups of compact surfaces with boundary into classical simple Lie groups of Hermitian type. We relate work on the signature of the associated local systems of Atiyah-Patodi-Singer, to Burger-Iozzi-Wienhard's Toledo invariant. To measure the difference, we extend Atiyah-Patodi-Singer's rho invariant, initially defined on U(p), to discontinuous class functions, first on U(p,q), and then on other classical groups via embeddings into U(p,q). In this way, we present three different invariants -- signature, Toledo and rho invariant -- in a unifying way, which is a version of the classical signature formula of Atiyah-Patodi-Singer for manifolds with boundary.