CALCULATING HEEGAARD-FLOER HOMOLOGY BY COUNTING LATTICE POINTS IN TETRAHEDRA

摘要

We introduce a notion of complexity for Seifert homology spheres by establishing a correspondence between lattice point counting in tetrahedra and the Heegaard-Floer homology. This complexity turns out to be equivalent to a version of Casson invariant and it is monotone under a natural partial order on the set of Seifert homology spheres. Using this interpretation we prove that there are finitely many Seifert homology spheres with a prescribed Heegaard-Floer homology. As an application, we characterize L-spaces and weakly elliptic manifolds among Seifert homology spheres. Also, we list all the Seifert homology spheres up to complexity two.