Exotic 4-manifolds and Khovanov-Lipshitz-Sarkar homotopy type
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| Format: | Preprint |
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2026
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| _version_ | 1866914336026394624 |
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| author | Kauffman, Louis H. Nikonov, Igor M. Ogasa, Eiji |
| author_facet | Kauffman, Louis H. Nikonov, Igor M. Ogasa, Eiji |
| contents | We introduce a new diffeomorphism invariant of smooth compact oriented 4-manifolds $X$ with a framed oriented 1-link $L$ in the boundary, where $L$ may be the empty set, and
call it {\it Khovanov-Lipshitz-Sarkar skein lasagna homotopy type} or {\it KLS lasagna homotopy type} $\mathcal E^{LS}_0(X,L)$. Our invariant assigns to a smooth structure a stable homotopy type of a CW complex.
Our new invariant is not weaker than KR lasagna module, which were defined by Morrison, Walker and Wedrich.
For a pair $(X,L)$ such that $L\neq\emptyset$, our new invariant, KLS lasagna homotopy type, is stronger than the Khovanov-Rozansky $\mathfrak{gl}_2$ skein lasagna modules or KR lasagna modules. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_13462 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exotic 4-manifolds and Khovanov-Lipshitz-Sarkar homotopy type Kauffman, Louis H. Nikonov, Igor M. Ogasa, Eiji Geometric Topology 57K10, 57K18, 57K41 We introduce a new diffeomorphism invariant of smooth compact oriented 4-manifolds $X$ with a framed oriented 1-link $L$ in the boundary, where $L$ may be the empty set, and call it {\it Khovanov-Lipshitz-Sarkar skein lasagna homotopy type} or {\it KLS lasagna homotopy type} $\mathcal E^{LS}_0(X,L)$. Our invariant assigns to a smooth structure a stable homotopy type of a CW complex. Our new invariant is not weaker than KR lasagna module, which were defined by Morrison, Walker and Wedrich. For a pair $(X,L)$ such that $L\neq\emptyset$, our new invariant, KLS lasagna homotopy type, is stronger than the Khovanov-Rozansky $\mathfrak{gl}_2$ skein lasagna modules or KR lasagna modules. |
| title | Exotic 4-manifolds and Khovanov-Lipshitz-Sarkar homotopy type |
| topic | Geometric Topology 57K10, 57K18, 57K41 |
| url | https://arxiv.org/abs/2602.13462 |