On computation of morphism spaces and a direct limit of the bordered Floer homology of knot complements

2015/05/27 by Lee, Jaepil
#53D40 #57M25 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1505.07223

Abstract

In the bordered Floer theory, gluing thickened torus of positive meridional Dehn twist to the boundary of a knot complement result in the knot complement of increased framing. For a fixed knot K, we construct a direct system of positively framed knot complements and study the direct limit. We also study the morphism space between two type-DD modules, and derive type-DA morphisms from DD morphisms to derive the direct system maps. In addition, we introduce a direct limit invariant from the direct system which can detect non-unstable chains in the type-D module of a knot complement, if the type-D modules of the direct system are obtained by algorithm of Lipshitz, Ozsvath and Thurston.

Related

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• An introduction to knot Floer homology and curved bordered algebras
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