Relative genus bounds in indefinite four-manifolds

Manolescu, Ciprian and Marengon, Marco and Piccirillo, Lisa (2024) Relative genus bounds in indefinite four-manifolds. MATHEMATISCHE ANNALEN, Publis. ISSN 0025-5831

Preview

Text 2012.12270v2.pdf Available under License Creative Commons Attribution. Download (552kB) | Preview

Abstract

Given a closed four-manifold X with an indefinite intersection form, we consider smoothly embedded surfaces in X \ ˚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.

Actions (login required)

Edit Item