On the kernel of the surgery map (Intelligence of Low-dimensional Topology)

Abstract

A Jacobi diagram gives a clasper in the trivial homology cylinder, and then one obtains another homology cylinder by surgery along the clasper. This procedure defines a homomorphism Sn: A[c, n] → YnLCg, ₁/Yn+1 between abelian groups. Sato, Suzuki, and the author [15, 16] constructed a homomorphism on YnLCg, ₁/Yn+1, and gave an application to the study of the surgery map Sn. The purpose of this article is to review the results in [16] and introduce related works on the surgery map.