1998•International Journal of MathematicsRequires access

FLOER HOMOLOGY AND INVARIANTS OF HOMOLOGY COBORDISM

Nikolai Saveliev

Abstract

By using surgery techniques, we compute Floer homology for certain classes of integral homology 3-spheres homology cobordant to zero. We prove that Floer homology is two-periodic for all these manifolds. Based on this fact, we introduce a new integer valued invariant of integral homology 3-spheres. Our computations suggest its homology cobordism invariance.

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Key concepts: Mathematics, Floer homology, Morse homology, Cellular homology, Cobordism, Khovanov homology, Homology (biology), Mayer–Vietoris sequence