2016/01/27 by Maciej Borodzik, Eugene Gorsky · 13 citations
Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #Bounding overwatch #Cobordism #Combinatorics #Concordance #Floer homology #Geometric and Algebraic Topology #Gravitational singularity #Heegaard splitting #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Linking number #Mathematical analysis #Mathematical physics #Mathematics #Pure mathematics #math.AG #math.GT
paper · pdf · doi:10.1512/iumj.2018.67.7375
published in Indiana University Mathematics Journal 67(3), 1039-1083 (Indiana University) · 35 pages, 7 figures
arxiv created 2016/01/27 · openalex created_date 2016/06/24 · openalex publication_date 2018/01/01 · arxiv updated 2018/07/03 · openalex updated_date 2026/08/05
An immersed concordance between two links is a concordance with possible\nself-intersections. Given an immersed concordance we construct a smooth\nfour-dimensional cobordism between surgeries on links. By applying\nd-invariant inequalities for this cobordism we obtain inequalities between\nthe H-functions of links, which can be extracted from the link Floer homology\npackage. As an application we show a Heegaard Floer theoretical criterion for\nbounding the splitting number of links. The criterion is especially effective\nfor L-space links, and we present an infinite family of L-space links with\nvanishing linking numbers and arbitrary large splitting numbers. We also show a\nsemicontinuity of the H-function under \δ-constant deformations of\nsingularities with many branches.