Calculating Heegaard-Floer Homology by Counting Lattice Points in Tetrahedra

Mahir Bilen Can; Cagri Karakurt

doi:10.1007/s10474-014-0432-2

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arXiv · 1211.4934

Calculating Heegaard-Floer Homology by Counting Lattice Points in Tetrahedra

Mahir Bilen Can·Cagri Karakurt

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Abstract

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 manifolds among Seifert homology spheres. Also, we list all the Seifert homology spheres up to complexity two.

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BibTeX RIS

Mahir Bilen Can, Cagri Karakurt. 2013-02-21. Calculating Heegaard-Floer Homology by Counting Lattice Points in Tetrahedra. https://doi.org/10.1007/s10474-014-0432-2

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