Augmentations and sheaves for links
Honghao Gao
TL;DR
This paper explores the relationship between augmentations and sheaves in the context of framed oriented links, establishing a bijective correspondence after removing certain sheaves, thus advancing the understanding of link invariants.
Contribution
It introduces a bijective correspondence between augmentations of the framed cord algebra and simple sheaves micro-supported along the conormal bundle of the link, refining previous relations.
Findings
More sheaves than augmentations are found in this setup.
A bijective correspondence is established after removing sporadic sheaves.
The work enhances the understanding of link invariants via sheaf theory.
Abstract
We study the relation between augmentations and sheaves in the context of framed oriented links. In this set up, we find slightly more sheaves than augmentations. After removing the sporadic sheaves, we construct a bijective correspondence between augmentations of the framed cord algebra and simple sheaves that are micro-supported along the conormal bundle of the link.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Geometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology