
TL;DR
This paper explores a new relationship between Giller's invariant of Montesinos twins and the Seiberg-Witten invariant, revealing connections between knot invariants and 4-manifold topology.
Contribution
It establishes a link between Giller's invariant for Montesinos twins and the Seiberg-Witten invariant of certain 4-manifold exteriors, extending understanding of knot invariants.
Findings
Giller's invariant relates to the Seiberg-Witten invariant for Montesinos twins.
The invariant is symmetric, unlike the Alexander polynomial.
The work connects knot invariants with 4-manifold topology.
Abstract
C. Giller proposed an invariant of ribbon 2-knots in S^4 based on a type of skein relation for a projection to R^3. In certain cases, this invariant is equal to the Alexander polynomial for the 2-knot. Giller's invariant is, however, a symmetric polynomial -- which the Alexander polynomial of a 2-knot need not be. After modifying a 2-knot into a Montesinos twin in a natural way, we show that Giller's invariant is related to the Seiberg-Witten invariant of the exterior of the twin, glued to the complement of a fiber in E(2).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Connective tissue disorders research · Homotopy and Cohomology in Algebraic Topology
