Relative genus bounds in indefinite 4-manifolds

Marco Marengon (Max Planck Institute for Mathematics)

09-Apr-2021, 15:00-16:15 (3 years ago)

Abstract: Given a closed 4-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X-int(B^4), with boundary a given knot K in the 3-sphere. We give several methods to bound the genus of such surfaces in a fixed homology class. Our techniques include adjunction inequalities from Heegaard Floer homology and the Bauer-Furuta invariants, and the 10/8 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disc) in a 4-manifold and show that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds. This is joint work with Ciprian Manolescu and Lisa Piccirillo.

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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