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The Groups <italic>G</italic>2<italic>n</italic> with Additional Structures.
- Source :
-
Mathematical Notes . Mar2018, Vol. 103 Issue 3/4, p593-609. 17p. - Publication Year :
- 2018
-
Abstract
- In the paper [1], V. O. Manturov introduced the groups <italic>G</italic><italic>k</italic><italic>n</italic> depending on two natural parameters <italic>n</italic> > <italic>k</italic> and naturally related to topology and to the theory of dynamical systems. The group <italic>G</italic>2<italic>n</italic>, which is the simplest part of <italic>G</italic><italic>k</italic><italic>n</italic>, is isomorphic to the group of pure free braids on n strands. In the present paper, we study the groups <italic>G</italic>2<italic>n</italic> supplied with additional structures-parity and points; these groups are denoted by <italic>G</italic>2<italic>n</italic>,<italic>p</italic> and <italic>G</italic>2<italic>n</italic>,<italic>d</italic>. First,we define the groups <italic>G</italic>2<italic>n</italic>,<italic>p</italic> and <italic>G</italic>2<italic>n</italic>,<italic>d</italic>, then study the relationship between the groups <italic>G</italic>2<italic>n</italic>, <italic>G</italic>2<italic>n</italic>,<italic>p</italic>, and <italic>G</italic>2<italic>n</italic>,<italic>d</italic>. Finally, we give an example of a braid on <italic>n</italic> + 1 strands, which is not the trivial braid on <italic>n</italic> + 1 strands, by using a braid on n strands with parity. After that, the author discusses links in <italic>S</italic><italic>g</italic> × <italic>S</italic>1 that can determine diagrams with points; these points correspond to the factor S1 in the product <italic>S</italic><italic>g</italic> × <italic>S</italic>1. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00014346
- Volume :
- 103
- Issue :
- 3/4
- Database :
- Academic Search Index
- Journal :
- Mathematical Notes
- Publication Type :
- Academic Journal
- Accession number :
- 129209352
- Full Text :
- https://doi.org/10.1134/S0001434618030264