Local moves on knots and products of knots

Louis H. Kauffman, and Eiji Ogasa. "Local moves on knots and products of knots." Banach Center Publications 103.1 (2014): 159-209. <http://eudml.org/doc/286374>.

@article{LouisH2014,
abstract = {We show a relation between products of knots, which are generalized from the theory of isolated singularities of complex hypersurfaces, and local moves on knots in all dimensions. We discuss the following problem. Let K be a 1-knot which is obtained from another 1-knot J by a single crossing change (resp. pass-move). For a given knot A, what kind of relation do the products of knots, K ⊗ A and J ⊗ A, have? We characterize these kinds of relation between K ⊗ A and J ⊗ A by using local moves on high dimensional knots. We also discuss a connection between local moves and knot invariants. We show a new form of identities for knot polynomials associated with a local move.},
author = {Louis H. Kauffman, Eiji Ogasa},
journal = {Banach Center Publications},
keywords = {local moves on 1-knots; local moves on high dimensional knots; crossing-changes on 1-links; pass-moves on 1-links; products of knots; pass-moves on high dimensional links; twist-moves on high dimensional links; branched cyclic covering spaces; Seifert hypersurfaces; Seifert matrices},
language = {eng},
number = {1},
pages = {159-209},
title = {Local moves on knots and products of knots},
url = {http://eudml.org/doc/286374},
volume = {103},
year = {2014},
}

TY - JOUR
AU - Louis H. Kauffman
AU - Eiji Ogasa
TI - Local moves on knots and products of knots
JO - Banach Center Publications
PY - 2014
VL - 103
IS - 1
SP - 159
EP - 209
AB - We show a relation between products of knots, which are generalized from the theory of isolated singularities of complex hypersurfaces, and local moves on knots in all dimensions. We discuss the following problem. Let K be a 1-knot which is obtained from another 1-knot J by a single crossing change (resp. pass-move). For a given knot A, what kind of relation do the products of knots, K ⊗ A and J ⊗ A, have? We characterize these kinds of relation between K ⊗ A and J ⊗ A by using local moves on high dimensional knots. We also discuss a connection between local moves and knot invariants. We show a new form of identities for knot polynomials associated with a local move.
LA - eng
KW - local moves on 1-knots; local moves on high dimensional knots; crossing-changes on 1-links; pass-moves on 1-links; products of knots; pass-moves on high dimensional links; twist-moves on high dimensional links; branched cyclic covering spaces; Seifert hypersurfaces; Seifert matrices
UR - http://eudml.org/doc/286374
ER -