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SUMMARY:Christoforos Neofytidis (Ohio State University)
DTSTART:20210112T180000Z
DTEND:20210112T190000Z
DTSTAMP:20260423T004637Z
UID:OSUGGT/19
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSUGGT/19/">
 Endomorphisms of mapping tori</a>\nby Christoforos Neofytidis (Ohio State 
 University) as part of Ohio State Topology and Geometric Group Theory Semi
 nar\n\n\nAbstract\nOne of the most fundamental results in 3-dimensional to
 pology\, proved in works of Gromov\, Mostow\, Wang and Waldhausen\, is tha
 t any self-map of non-zero degree of a mapping torus of a closed hyperboli
 c surface is homotopic to a homeomorphism if and only if the monodromy is 
 not periodic. Key properties for the proof were the existence of hyperboli
 c structures or of non-vanishing semi-norms (such as the simplicial volume
 ). Using Algebra\, we give a new\, unified proof and generalise the above 
 result in every dimension\, by replacing the hyperbolic surface with a cor
 responding higher dimensional aspherical manifold. More generally\, we wil
 l classify in terms of Hopf-type properties mapping tori of residually fin
 ite Poincaré Duality groups with non-zero Euler characteristic. It turns 
 out that the rigidity behavior of these mapping tori with trivial center i
 s similar to that of non-elementary torsion-free hyperbolic groups.\n
LOCATION:https://researchseminars.org/talk/OSUGGT/19/
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