Embedding and bounding geometrically rational homology 3-spheres

Alan Reid (Rice University)

01-Apr-2022, 15:00-16:15 (24 months ago)

Abstract: Bordism properties of closed manifolds have been a classical and important topic in topology; for example it is a classical result of Rohklin that all closed orientable 3-manifolds bound a compact 4-manifold. In the context of hyperbolic manifolds, a natural geometric version of bordism is that of bounding geometrically: namely whether a connected closed orientable hyperbolic n-manifold M could arise as the totally geodesic boundary of a compact hyperbolic (n+1)-manifold W. In work with Long (from 2000) we showed that there are infinitely many closed orientable hyperbolic n-manifolds that bound geometrically. One feature of our construction is that all examples produced in dimension 3 have b_1>0. This led to the question of whether there are rational homology 3-spheres that bound geometrically. In this talk we describe a construction of infinitely many such rational homology 3-spheres.

algebraic geometryanalysis of PDEsalgebraic topologycomplex variablesdifferential geometrygeneral topologygeometric topologyK-theory and homologymetric geometrysymplectic geometry

Audience: researchers in the topic


CRM - Séminaire du CIRGET / Géométrie et Topologie

Series comments: Hybrid seminar of geometry and topology. Laboratory : CIRGET - www.cirget.uqam.ca The homepage of the seminar is www.cirget.uqam.ca/fr/seminaires.html

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Organizers: Julien Keller*, Duncan McCoy
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