Virtual Links in Arbitrary Dimensions
Geometric Topology
2015-09-04 v1
Abstract
We define a generalization of virtual links to arbitrary dimensions by extending the geometric definition due to Carter et al. We show that many homotopy type invariants for classical links extend to invariants of virtual links. We also define generalizations of virtual link diagrams and Gauss codes to represent virtual links, and use such diagrams to construct a combinatorial biquandle invariant for virtual -links. In the case of -links, we also explore generalizations of Fox-Milnor movies to the virtual case. In addition, we discuss definitions extending the notion of welded links to higher dimensions.
Keywords
Cite
@article{arxiv.1509.01174,
title = {Virtual Links in Arbitrary Dimensions},
author = {Blake Winter},
journal= {arXiv preprint arXiv:1509.01174},
year = {2015}
}
Comments
To appear in Journal of Knot Theory and its Ramifications. All results are from the author's dissertation, available at arXiv:1407.0421