  Surgery triangles are an important computational tool in Floer homology.
Given a connected oriented surface $\Sigma$, we consider the abelian group
$K(\Sigma)$ generated by bordered 3-manifolds with boundary $\Sigma$, modulo
the relation that the three manifolds involved in any surgery triangle sum to
zero. We show that $K(\Sigma)$ is a finitely generated free abelian group and
compute its rank. We also construct an explicit basis and show that it
generates all bordered 3-manifolds in a certain stronger sense. Our basis is
strictly contained in another finite generating set which was constructed
previously by Baldwin and Bloom. As a byproduct we confirm a conjecture of
Blokhuis and Brouwer on spanning sets for the binary symplectic dual polar
space.
