Characterising knots by their branched coverings
Luisa Paoluzzi (AMU)
TL;DR
This paper discusses the problem of identifying knots through their cyclic branched coverings, providing insights and methods relevant to knot theory and 3-manifold topology.
Contribution
It offers a detailed exploration of how knots can be characterized by their branched coverings, contributing to the understanding of knot invariants and classification.
Findings
Cyclic branched coverings can distinguish certain classes of knots.
Methods for analyzing knot properties via their coverings are developed.
Open problems in knot characterization are discussed.
Abstract
These are the notes for a mini-course on the problem of determining knots by means of their cyclic branched coverings given at the Workshop on Branched Covers held at IMUS in Seville from November 17 to 21, 2025.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic Geometry and Number Theory · Geometry and complex manifolds