Relative genus bounds in indefinite four-manifolds

2020/12/22 by Manolescu, Ciprian, Marengon, Marco, Piccirillo, Lisa · 2 citations
#57K10 #57K18 #57K40 #57K41 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2012.12270

Abstract

Given a closed four-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X ∖ int(B⁴), with boundary a knot K ⊂ S³. We give several methods to bound the genus of such surfaces in a fixed homology class. Our tools include adjunction inequalities and the 10/8 + 4 theorem. In particular, we present obstructions to a knot being H-slice (that is, bounding a null-homologous disk) in a four-manifold and show that the set of H-slice knots can detect exotic smooth structures on closed 4-manifolds.

Cited by

• Constructing knots with low rational genera
• Simply slicing knots

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