English

Alexander's and Markov's theorems in dimension four

Geometric Topology 2016-09-06 v1

Abstract

Alexander's and Markov's theorems state that any link type in R3R^3 is represented by a closed braid and that such representations are related by some elementary operations called Markov moves. We generalize the notion of a braid to that in 4-dimensional space and establish an analogue of these theorems.

Keywords

Cite

@article{arxiv.math/9407217,
  title  = {Alexander's and Markov's theorems in dimension four},
  author = {Seiichi Kamada},
  journal= {arXiv preprint arXiv:math/9407217},
  year   = {2016}
}

Comments

4 pages

R2 v1 2026-07-22T17:54:58.065Z