From knots to four-manifolds

Fuente: arXiv
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Main Author: Manolescu, Ciprian
Format: Preprint
Published: 2026
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_version_ 1866912986184024064
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