2021/10/18 by Hokuto Konno, Konno, Hokuto, Jin Miyazawa +3 · 1 citation
Mathematics · Computer Science · #Geometric and Algebraic Topology #semigroups and automata theory #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2110.09258
We establish a version of Seiberg--Witten Floer K-theory for knots, as well as a version of Seiberg-Witten Floer K-theory for 3-manifolds with involution. The main theorems are 10/8-type inequalities for knots and for involutions. The 10/8-inequality for knots yields numerous applications to knots, such as lower bounds on stabilizing numbers and relative genera. We also give obstructions to extending involutions on 3-manifolds to 4-manifolds, and detect non-smoothable involutions on 4-manifolds with boundary.