Invariants of Montesinos Twins
Geometric Topology
2012-12-06 v1 Differential Geometry
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).
Keywords
Cite
@article{arxiv.1212.1147,
title = {Invariants of Montesinos Twins},
author = {Adam C. Knapp},
journal= {arXiv preprint arXiv:1212.1147},
year = {2012}
}