SU\G(𝔸)/K·U

Functoriality of Khovanov homology

Pierre Vogel

Type: Article

Publication Date: 2020-02-04

Citations: 7

DOI: https://doi.org/10.1142/s0218216520500200

Abstract

In this paper, we prove that every Khovanov homology associated to a Frobenius algebra of rank 2 can be modified in such a way as to produce a TQFT on oriented links, that is a monoidal functor from the category of cobordisms of oriented links to the homotopy category of complexes.

Locations

  • arXiv (Cornell University) - View - PDF
  • Journal of Knot Theory and Its Ramifications - View

Similar Works

Action Title Year Authors
+ Functoriality of Khovanov homology 2015 Pierre Vogel
+ Functoriality of Khovanov homology 2015 Pierre Vogel
+ PDF Chat On link homology theories from extended cobordisms 2010 Anna Beliakova
Emmanuel Wagner
+ PDF Chat Fixing the functoriality of Khovanov homology: A simple approach 2021 Taketo Sano
+ On a triply graded Khovanov homology 2015 Krzysztof K. Putyra
+ PDF Chat On a triply graded Khovanov homology 2016 Krzysztof K. Putyra
+ On a triply graded Khovanov homology 2015 Krzysztof K. Putyra
+ Odd Khovanov homology and higher representation theory 2023 LĂ©o Schelstraete
Pedro Vaz
+ PDF Chat Khovanov’s homology for tangles and cobordisms 2005 Dror Bar-Natan
+ PDF Chat The homotopy theory of Khovanov homology 2014 Brent Everitt
Paul Turner
+ A 2-category of chronological cobordisms and odd Khovanov homology 2013 Krzysztof K. Putyra
+ A 2-category of chronological cobordisms and odd Khovanov homology 2013 Krzysztof K. Putyra
+ PDF Chat Torsion of Khovanov homology 2014 Alexander N. Shumakovitch
+ A link invariant related to Khovanov homology and knot Floer homology 2018 Akram Alishahi
Nathan Dowlin
+ PDF Chat An invariant of link cobordisms from Khovanov homology 2004 Magnus Jacobsson
+ Khovanov type homologies and Frobenius extensions 2006 Herme Soto
Stella Huérfano
+ Homotopical Khovanov homology 2015 Vassily Olegovich Manturov
Igor Nikonov
+ PDF Chat Homotopical Khovanov homology 2015 Vassily Olegovich Manturov
Igor Nikonov
+ Homotopical Khovanov homology 2015 Vassily Olegovich Manturov
Igor Nikonov
+ Khovanov homology and categorification of skein modules 2018 Hoel Queffélec
Paul Wedrich

Works That Cite This (7)

Action Title Year Authors
+ PDF Chat Khovanov homotopy type, periodic links and localizations 2021 Maciej Borodzik
Wojciech Politarczyk
Marithania Silvero
+ gl(2) foams and the Khovanov homotopy type 2021 Vyacheslav Krushkal
Paul Wedrich
+ PDF Chat A deformation of Robert-Wagner foam evaluation and link homology 2024 Mikhail Khovanov
Nitu Kitchloo
+ PDF Chat Link homology and Frobenius extensions II 2021 Mikhail Khovanov
Louis-Hadrien Robert
+ PDF Chat Fixing the functoriality of Khovanov homology: A simple approach 2021 Taketo Sano
+ Movie moves for framed foams from multijet transversality 2024 Hoel Queffélec
Kevin Walker
+ Khovanov homotopy type, periodic links and localizations 2018 Maciej Borodzik
Wojciech Politarczyk
Marithania Silvero

Works Cited by This (16)

Action Title Year Authors
+ Frobenius Algebras and 2D Topological Quantum Field Theories 2003 Joachim Kock
+ Khovanov-Jacobsson numbers and invariants of surface-knots derived from Bar-Natan’s theory 2006 Kokoro Tanaka
+ PDF Chat An invariant of tangle cobordisms 2005 Mikhail Khovanov
+ PDF Chat sl(2) tangle homology with a parameter and singular cobordisms 2008 Carmen Caprau
+ PDF Chat Khovanov homology and the slice genus 2010 Jacob Rasmussen
+ PDF Chat Khovanov’s homology for tangles and cobordisms 2005 Dror Bar-Natan
+ PDF Chat Link homology and Frobenius extensions 2006 Mikhail Khovanov
+ PDF Chat A functor-valued invariant of tangles 2002 Mikhail Khovanov
+ REIDEMEISTER MOVES FOR SURFACE ISOTOPIES AND THEIR INTERPRETATION AS MOVES TO MOVIES 1993 J. Scott Carter
Masahico Saito
+ PDF Chat A categorification of the Jones polynomial 2000 Mikhail Khovanov