Homology cobordism and knot concordance

Abstract: The 0-surgeries of two knots K1 and K2 are homology cobordant rel meridians if there exists an integer homology cobordism X between them such that the two positive knot meridians are in the same homology class of X. It is a natural question to ask: if two knots have the “same” 0-surgeries in this sense, must they be smoothly concordant? We give a pair of rationally slice knots as counterexample, with one of concordance order two and the other of infinite order, and along the way expand upon a Floer homology technique for obstructing torsion in the smooth concordance group first introduced by Hom, Kang, Park, and Stoffregen.

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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