On links in S_g × S¹ and its invariants

2021/04/17 by Kim, Seongjeong
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2104.08573

Abstract

A virtual knot, which is one of generalizations of knots in ℝ³ (or S³), is, roughly speaking, an embedded circle in thickened surface S_g × I. In this talk we will discuss about knots in 3 dimensional S_g × S¹. We introduce basic notions for knots in S_g × S¹, for example, diagrams, moves for diagrams and so on. For knots in S_g × S¹ technically we lose over/under information, but we will have information how many times the knot rotates along S¹. We will discuss the geometric meaning of the rotating information and how to construct invariants by using the "rotating" information.

Related

• Knots in S_g × S¹ and winding parities
• Knots in S_g × S¹, their essential diagrams and virtual knots
• Virtual Covers of Links
• Relating virtual knot invariants to links in \mathbbS³
• A twisted link invariant derived from a virtual link invariant