Rack Module Enhancements of Counting Invariants
Geometric Topology
2010-08-04 v1 Quantum Algebra
Abstract
We introduce a modified rack algebra Z[X] for racks X with finite rack rank N. We use representations of Z[X] into rings, known as rack modules, to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide computations and examples to show that the new invariants are strictly stronger than the unenhanced counting invariant and are not determined by the Jones or Alexander polynomials.
Keywords
Cite
@article{arxiv.1008.0114,
title = {Rack Module Enhancements of Counting Invariants},
author = {Aaron Haas and Garret Heckel and Sam Nelson and Jonah Yuen and Qingcheng Zhang},
journal= {arXiv preprint arXiv:1008.0114},
year = {2010}
}
Comments
14 pages