English

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

R2 v1 2026-06-21T15:55:32.706Z