Classification of string links up to self delta-moves and concordance

Yasuhara, Akira

doi:10.2140/agt.2009.9.265

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Classification of string links up to self delta-moves and concordance

Akira Yasuhara

Algebraic & Geometric Topology 9 (2009) 265–275

DOI: 10.2140/agt.2009.9.265

Abstract

For an $n$ –component string link, the Milnor’s concordance invariant is defined for each sequence $I = i_{1} i_{2} \dots i_{m} (i_{j} \in {1, \dots, n})$ . Let $r (I)$ denote the maximum number of times that any index appears. We show that two string links are equivalent up to self $Δ$ –moves and concordance if and only if their Milnor invariants coincide for all sequences $I$ with $r (I) \leq 2$ .

Keywords

string link, $\Delta$–move, self $\Delta$–move, link-homotopy, concordance, self $\Delta$–equivalence, Milnor invariant

Mathematical Subject Classification 2000

Primary: 57M25, 57M27

References

Publication

Received: 6 July 2008

Revised: 26 November 2008

Accepted: 19 December 2008

Published: 13 February 2009

Authors

Akira Yasuhara
Tokyo Gakugei University Department of Mathematics Koganeishi Tokyo 184–8501 Japan

Volume 9, issue 1 (2009)