From knots to four-manifolds

Ciprian Manolescu

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arXiv · 2601.05425

From knots to four-manifolds

Ciprian Manolescu

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Abstract

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.

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BibTeX RIS

Ciprian Manolescu. 2026-01-08. From knots to four-manifolds. https://arxiv.org/abs/2601.05425

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