Work

Projective Rigidity of Once-Punctured Torus Bundles via Twisted Invariants

Year: 2025

Type: article

Abstract: 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 the Wada Invariant 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 $$\text {PGL}(4,\mathbb {R})$$ 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 from the monodromy action of the once-punctured torus bundle on cohomology.

Source: Geometriae Dedicata

DOI: 10.1007/s10711-025-01039-w

Author: Charles Daly

Institutions: Brown University, Max Planck Institute for Mathematics in the Sciences

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,090

Funders: Universitat Autònoma de Barcelona, Max-Planck-Institut für Mathematik in den Naturwissenschaften