Relative genus bounds in indefinite 4-manifolds

Description of video

Date: 10/8/21
Speaker :Marco Marengon

AGDT Seminar


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.


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