Endomorphisms of mapping tori
Christoforos Neofytidis

TL;DR
This paper classifies certain mapping tori of Poincaré Duality groups using Hopf properties, extending known results for 3-manifolds and applying to hyperbolic group rigidity.
Contribution
It provides a new classification framework for mapping tori of Poincaré Duality groups based on Hopf properties, generalizing previous 3-manifold results.
Findings
Classification of mapping tori with non-zero Euler characteristic
Extension of rigidity results to these mapping tori
New proof of classification for fibered 3-manifolds
Abstract
We classify in terms of Hopf-type properties mapping tori of residually finite Poincar\'e Duality groups with non-zero Euler characteristic. This generalises and gives a new proof of the analogous classification for fibered 3-manifolds. Various applications are given. In particular, we deduce that rigidity results for Gromov hyperbolic groups hold for the above mapping tori with trivial center.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Homotopy and Cohomology in Algebraic Topology
