A combinatorial matrix in 3-manifold theory

Ki Hyoung Ko and Lawrence Smolinsky

Vol. 149 (1991), No. 2, 319–336

DOI: 10.2140/pjm.1991.149.319

Abstract

In this paper we study a combinatorial matrix considered by W. B. R. Lickorish. We prove a conjecture by Lickorish that completes his topological and combinatorial proof of the existence of the Witten-Reshetikhin-Turaev 3-manifold invariants. We derive a recursive formula for the determinant of the matrix and discover some interesting numerical relations.

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57N10

Milestones

Received: 23 February 1990

Revised: 5 April 1990

Published: 1 June 1991