From knots to four-manifolds
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912986184024064 |
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| author | Manolescu, Ciprian |
| author_facet | Manolescu, Ciprian |
| contents | This is a survey article about the connections between knot theory and four-dimensional topology. Every four-manifold can be represented in terms of a link, by a Kirby diagram. This point of view has led to progress in computing invariants of smooth four-manifolds that can detect exotic structures. We explain how this was done in two contexts: Heegaard Floer theory and skein lasagna modules. We also describe a program to understand four-manifolds through the properties of knots on their boundaries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05425 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | From knots to four-manifolds Manolescu, Ciprian Geometric Topology 57K10, 57K18, 57K40, 57K41 This is a survey article about the connections between knot theory and four-dimensional topology. Every four-manifold can be represented in terms of a link, by a Kirby diagram. This point of view has led to progress in computing invariants of smooth four-manifolds that can detect exotic structures. We explain how this was done in two contexts: Heegaard Floer theory and skein lasagna modules. We also describe a program to understand four-manifolds through the properties of knots on their boundaries. |
| title | From knots to four-manifolds |
| topic | Geometric Topology 57K10, 57K18, 57K40, 57K41 |
| url | https://arxiv.org/abs/2601.05425 |