2019/10/17 by Ciprian Manolescu, Marco Marengon, Manolescu, Ciprian +5 · 2 citations
Mathematics · #57M25 (Secondary) #57M27 (Primary) #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1910.08195
openalex publication_date 2019/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the definition of Khovanov-Lee homology to links in connected sums of S1 × S2's, and construct a Rasmussen-type invariant for null-homologous links in these manifolds. For certain links in S1 × S2, we compute the invariant by reinterpreting it in terms of Hochschild homology. As applications, we prove inequalities relating the Rasmussen-type invariant to the genus of surfaces with boundary in the following four-manifolds: B2 × S2, S1 × B3, \mathbbCP2, and various connected sums and boundary sums of these. We deduce that Rasmussen's invariant also gives genus bounds for surfaces inside homotopy 4-balls obtained from B4 by Gluck twists. Therefore, it cannot be used to prove that such homotopy 4-balls are non-standard.