# A new proof of Markov's braid theorem

Banach Center Publications (1998)

- Volume: 42, Issue: 1, page 409-419
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topTraczyk, Paweł. "A new proof of Markov's braid theorem." Banach Center Publications 42.1 (1998): 409-419. <http://eudml.org/doc/208820>.

@article{Traczyk1998,

abstract = {The purpose of this paper is to introduce a new proof of Markov's braid theorem, in terms of Seifert circles and Reidemeister moves. This means that the proof will be of combinatorial and essentially 2-dimensional nature. One characteristic feature of our approach is that nowhere in the proof will we use or refer to the braid axis. This allows for greater flexibility in various transformations of the diagrams considered. Other proofs of Markov's theorem can be found in [2], [3], [4] and [5].},

author = {Traczyk, Paweł},

journal = {Banach Center Publications},

keywords = {Markov moves; braid},

language = {eng},

number = {1},

pages = {409-419},

title = {A new proof of Markov's braid theorem},

url = {http://eudml.org/doc/208820},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Traczyk, Paweł

TI - A new proof of Markov's braid theorem

JO - Banach Center Publications

PY - 1998

VL - 42

IS - 1

SP - 409

EP - 419

AB - The purpose of this paper is to introduce a new proof of Markov's braid theorem, in terms of Seifert circles and Reidemeister moves. This means that the proof will be of combinatorial and essentially 2-dimensional nature. One characteristic feature of our approach is that nowhere in the proof will we use or refer to the braid axis. This allows for greater flexibility in various transformations of the diagrams considered. Other proofs of Markov's theorem can be found in [2], [3], [4] and [5].

LA - eng

KW - Markov moves; braid

UR - http://eudml.org/doc/208820

ER -

## References

top- [1] J.W. Alexander, A Lemma on Systems of Knotted Curves, Proc. Nat. Acad. Sci. 9 (1923), 93-95.
- [2] D. Bennequin, Entrelacements et équations de Pfaff, Astérisque 107-108 (1983), 87-161.
- [3] J. Birman, Braids, links and the mapping class groups, Annals of Math. Stud. 82, Princeton University Press, 1974.
- [4] A.A. Markov, Über die freie Äquivalenz geschlossener Zöpfe, Recueil Mathématique Moscou 1 (1935).
- [5] H.R. Morton, Threading knot diagrams, Math. Proc. Camb. Phil. Soc. 99 (1986), 247-260. Zbl0595.57007
- [6] P. Vogel, Representation of links by braids: A new algorithm, Comment. Math. Helvetici 65 (1990), 104-113. Zbl0703.57004
- [7] S. Yamada, The minimal number of Seifert circles equals the braid index of a link, Invent. Math. 89 (1987), 347-356. Zbl0634.57004

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.