Khovanov skein lasagna modules with $1$-dimensional inputs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914078847401984 |
|---|---|
| author | Ren, Qiuyu Sullivan, Ian Wedrich, Paul Willis, Michael Zhang, Melissa |
| author_facet | Ren, Qiuyu Sullivan, Ian Wedrich, Paul Willis, Michael Zhang, Melissa |
| contents | We construct a variant of Khovanov skein lasagna modules, which takes the Khovanov homology in connected sums of $S^1\times S^2$ defined by Rozansky and Willis as the input link homology. To carry out the construction, we prove functoriality of Rozansky-Willis's homology for cobordisms in a class of $4$-manifolds that we call $4$-dimensional relative $1$-handlebody complements, by using, as a bypass, an isomorphism proved by Sullivan--Zhang relating the Rozansky-Willis homology and the classical Khovanov skein lasagna module of links on the boundary of $D^2\times S^2$. Along the way, we also present new results on diffeomorphism groups, on Gluck twists for Khovanov skein lasagna modules, and on the functoriality of $\mathfrak{gl}_2$ foams. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Khovanov skein lasagna modules with $1$-dimensional inputs Ren, Qiuyu Sullivan, Ian Wedrich, Paul Willis, Michael Zhang, Melissa Geometric Topology Quantum Algebra 57K41 (Primary) 57K18, 57K16, 57R56 (Secondary) We construct a variant of Khovanov skein lasagna modules, which takes the Khovanov homology in connected sums of $S^1\times S^2$ defined by Rozansky and Willis as the input link homology. To carry out the construction, we prove functoriality of Rozansky-Willis's homology for cobordisms in a class of $4$-manifolds that we call $4$-dimensional relative $1$-handlebody complements, by using, as a bypass, an isomorphism proved by Sullivan--Zhang relating the Rozansky-Willis homology and the classical Khovanov skein lasagna module of links on the boundary of $D^2\times S^2$. Along the way, we also present new results on diffeomorphism groups, on Gluck twists for Khovanov skein lasagna modules, and on the functoriality of $\mathfrak{gl}_2$ foams. |
| title | Khovanov skein lasagna modules with $1$-dimensional inputs |
| topic | Geometric Topology Quantum Algebra 57K41 (Primary) 57K18, 57K16, 57R56 (Secondary) |
| url | https://arxiv.org/abs/2510.05273 |