Work

Bigrading the symplectic Khovanov cohomology

Year: 2023

Type: article

Abstract: We construct a well-defined relative second grading on symplectic Khovanov cohomology from holomorphic disc counting.We use a version of symplectic Khovanov cohomology defined for bridge diagrams rather than braids.We show that our second grading recovers the Jones grading of Khovanov homology up to an overall grading shift over any characteristic-zero field, through proving that the isomorphism of Abouzaid and Smith can be refined as an isomorphism between bigraded cohomology theories.The central idea of the proof is to construct an exact triangle for symplectic Khovanov cohomology that behaves similarly to the unoriented skein exact triangle for Khovanov homology.

Source: Algebraic & Geometric Topology

DOI: 10.2140/agt.2023.23.4057

Author: Zhechi Cheng

Institution: Wuhan University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funders: National Science Foundation, National Natural Science Foundation of China, Vetenskapsrådet, Wuhan University

Awards: Institut Mittag-Leffler, Family Floer Cohomology, FRG: Collaborative Research: Floer homotopy theory