Generation of sutured manifolds

Abstract

Given a compact, oriented, connected surface $F$, we show that the set of connected sutured manifolds $(M,{\hat{I}}^3)$ with $R_{\pm }({\hat{I}}^3)\cong F$ is generated by the product sutured manifold $(F,\partial F)\times [0,1]$ through surgery triads. This result has applications in Floer theories of $3$--manifolds. The special case when $F=D^2$ or $S^2$ has been a folklore theorem, which has already been used by experts before.

11 pages, 5 figures