Year: 2024
Type: preprint
Abstract: These notes are an introduction to knot theory from the perspective of surfaces. The notes cover fundamental concepts such as isotopies, Reidemeister moves, torus knots, and (orientable, connected) surfaces with one boundary component. They also present knot invariants defined through Seifert surfaces and their associated matrices, including the 3-genus, the Alexander polynomial, and the signature. Finally, starting from the notion of concordance and the connected sum operation, a group structure on the set of knots is introduced.
Source: arXiv (Cornell University)
Institution: University of Notre Dame
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4405957508