2024/11/07 by Charles Daly, Daly, Charles
Mathematics · #22 #51 #53 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2411.04431
openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we provide a means of certifying infinitesimal projective rigidity relative to the cusp for hyperbolic once punctured torus bundles in terms of twisted Alexander polynomials of representations associated to the holonomy. We also relate this polynomial to an induced action on the tangent space of the character variety of the free group of rank 2 into PGL(4,R) that arises from the holonomy of a hyperbolic once-punctured torus bundle. We prove the induced action on the tangent space of the character variety is the same as the group theoretic action that arises in the Lyndon Hochschild Serre spectral sequence on cohomology.