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 …

We introduce a notion of complexity for Sefiert homology spheres by establishing a
correspondence between lattice point counting in tethrahedra 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 in the set of Seifert homology spheres. Using this
interpretation we prove that there are finitely many Seifert homology spheres with prescribed
Heegaard-Floer homology. As an application, we characterize L-spaces and weakly elliptic …