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Instantons and Bar-Natan homology

Part of: Graph theory Differential topology

Published online by Cambridge University Press:  22 March 2021

P. B. Kronheimer  and
T. S. Mrowka
P. B. Kronheimer
Affiliation:
Department of Mathematics, Harvard University, 1 Oxford Street, Cambridge, MA02138, USAkronheim@math.harvard.edu
T. S. Mrowka
Affiliation:
Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA02139, USAmrowka@math.mit.edu
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Abstract

A spectral sequence is established whose $E_{2}$ page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence whose $E_{2}$ page is a characteristic-2 version of $F_{5}$ homology in Khovanov's classification.

Keywords

instantonsKhovanov homologyBar-Natan homologyknotsspectral sequence

MSC classification

Primary: 57R58: Floer homology
Secondary: 05C15: Coloring of graphs and hypergraphs
Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 3 , March 2021 , pp. 484 - 528
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Copyright
© The Author(s) 2021

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Footnotes

The work of the first author was supported by the National Science Foundation through NSF grants DMS-1405652 and DMS-1707924. The work of the second author was supported by NSF grants DMS-1406348 and DMS-1808794, and by a grant from the Simons Foundation, grant number 503559 TSM.

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