Bordered Floer Homology and a Meridional Class of Knot

TL;DR

This paper introduces an algorithm to compute the bordered Floer bimodule of a knot complement and its meridian, enabling the analysis of spin^c-summands in large Dehn surgery manifolds with arbitrary framing.

Contribution

It provides a novel algorithm for computing bordered Floer bimodules of knot complements and their meridians, extending to arbitrary framing.

Findings

Algorithm computes bordered Floer bimodule for knot complements and meridians.

Grading of the module determines spin^c-summands in large Dehn surgery.

Extension to arbitrary framing n enhances applicability.

Abstract

For a knot K and its knot Floer complex CFK^-(K), we introduce an algorithm to compute the bordered Floer bimodule of the complement of the knot and its meridian. The grading of the module computes spin^c-summands of a meridional knot in the large Dehn surgery manifold, which can be also extended to arbitrary framing n.