The decategorification of sutured Floer homology

By Stefan Friedl, Andr'as Juh'asz, Jacob Rasmussen. 2009

69 citations recorded by the source corpus.

We define a torsion invariant T for every balanced sutured manifold (M, γ), and show that it agrees with the Euler characteristic of sutured Floer homology (SFH). The invariant T is easily computed using Fox calculus. With the help of T, we prove that if (M, γ) is complementary to a Seifert surface of an alternating knot, then SFH(M, γ) is either 0 or ℤ in every Spinc structure. The torsion invariant T can also be used to show that a sutured manifold is not disc decomposable, and to distinguish between Seifert surfaces.

Subfields: Geometry and Topology, Mathematical Physics, Neurology

View Paper: https://www.semanticscholar.org/paper/f24c04910e49ba59a75e228fcc3765bf11efd9e7

Citations in the corpus

• Floer simple manifolds and L-space intervals (2015, unknown): “The Euler characteristic of the sutured Floer homology can be described as an appropriately formulated torsion [14].”