Local moves on knots and products of knots

• Autorzy: Louis H. Kauffman , Eiji Ogasa
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 57N15: Topology of E n , n -manifolds ( 4 n ∞ )
• 57N13: Topology of E 4 , 4 -manifolds
• 57N10: Topology of general 3 -manifolds

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2014
• Tom: 103
• Numer: 1
• Strony: 159-209

Daty

wydano

2014

Twórcy

autor

Louis H. Kauffman

• Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 South Morgan Street, Chicago, Illinois 60607-7045, USA

autor

Eiji Ogasa

• Computer Science, Meijigakuin University, Yokohama, Kanagawa, 244-8539, Japan

Identyfikatory

DOI

10.4064/bc103-0-7