On the kernel of the surgery map restricted to the 1-loop part

Yuta Nozaki, Masatoshi Sato, Masaaki Suzuki

Every homology cylinder is obtained from Jacobi diagrams by clasper surgery. The surgery map $\mathfrak{s}:{\mathcal{A}}_n^c\to Y_n{\mathcal{I}\mathcal{C}}_{g,1}/Y_{n+1}$ is surjective f…