TY - JOUR

T1 - Artin's braids, braids for three space, and groups σ n 4 and G n k

AU - Kim, S.

AU - Manturov, V. O.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - We construct a group σn4 corresponding to the motion of points in R 3 from the point of view of Delaunay triangulations. We study homomorphisms from pure braids on n strands to the product of copies of σn4. We will also study the group of pure braids in R 3, which is described by a fundamental group of the restricted configuration space of R 3, and define the group homomorphism from the group of pure braids in R 3 to σn4. At the end of this paper, we give some comments about relations between the restricted configuration space of R 3 and triangulations of the 3-dimensional ball and Pachner moves.

AB - We construct a group σn4 corresponding to the motion of points in R 3 from the point of view of Delaunay triangulations. We study homomorphisms from pure braids on n strands to the product of copies of σn4. We will also study the group of pure braids in R 3, which is described by a fundamental group of the restricted configuration space of R 3, and define the group homomorphism from the group of pure braids in R 3 to σn4. At the end of this paper, we give some comments about relations between the restricted configuration space of R 3 and triangulations of the 3-dimensional ball and Pachner moves.

KW - configuration space

KW - Pachner move

KW - Pure braid group

KW - representation of pure braid groups

KW - Triangulation of 3-dimensional spaces

UR - http://www.scopus.com/inward/record.url?scp=85069476015&partnerID=8YFLogxK

U2 - 10.1142/S0218216519500639

DO - 10.1142/S0218216519500639

M3 - Article

AN - SCOPUS:85069476015

VL - 28

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

SN - 0218-2165

IS - 10

M1 - 1950063

ER -