Homotopical Khovanov homology

被引:4
|
作者
Manturov, Vassily Olegovich [1 ,2 ]
Nikonov, Igor Mikhailovich [3 ,4 ]
机构
[1] Bauman Moscow State Tech Univ, Moscow, Russia
[2] Chelyabinsk State Univ, Lab Quantum Topol, Chelyabinsk, Russia
[3] Moscow MV Lomonosov State Univ, Dept Mech & Math, Moscow, Russia
[4] Natl Res Univ, Higher Sch Econ, Fac Business & Management, Moscow, Russia
关键词
Khovanov homology; homotopical grading;
D O I
10.1142/S0218216515410035
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We modify the definition of the Khovanov complex for oriented links in a thickening of an oriented surface to obtain a triply graded homological link invariant with a new homotopical grading.
引用
收藏
页数:17
相关论文
共 50 条
  • [1] Unoriented Khovanov Homology
    Baldridge, Scott
    Kauffman, Louis H.
    McCarty, Ben
    NEW YORK JOURNAL OF MATHEMATICS, 2022, 28 : 367 - 401
  • [2] NOT EVEN KHOVANOV HOMOLOGY
    Vaz, Pedro
    PACIFIC JOURNAL OF MATHEMATICS, 2020, 308 (01) : 223 - 256
  • [3] An Introduction to Khovanov Homology
    Kauffman, Louis H.
    KNOT THEORY AND ITS APPLICATIONS, 2016, 670 : 105 - 139
  • [4] Localization in Khovanov homology
    Stoffregen, Matthew
    Zhang, Melissa
    GEOMETRY & TOPOLOGY, 2024, 28 (04)
  • [5] Torsion of Khovanov homology
    Shumakovitch, Alexander N.
    FUNDAMENTA MATHEMATICAE, 2014, 225 : 343 - 364
  • [6] Rotors in Khovanov Homology
    MacColl, Joseph
    CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2016, 59 (01): : 159 - 169
  • [7] Odd Khovanov homology
    Ozsvath, Peter S.
    Rasmussen, Jacob
    Szabo, Zoltan
    ALGEBRAIC AND GEOMETRIC TOPOLOGY, 2013, 13 (03): : 1465 - 1488
  • [8] A refinement of Khovanov homology
    Lobb, Andrew
    Watson, Liam
    GEOMETRY & TOPOLOGY, 2021, 25 (04) : 1861 - 1917
  • [9] Evolutionary Khovanov homology
    Shen, Li
    Liu, Jian
    Wei, Guo-Wei
    AIMS MATHEMATICS, 2024, 9 (09): : 26139 - 26165
  • [10] Chromatic homology, Khovanov homology, and torsion
    Lowrance, Adam M.
    Sazdanovic, Radmila
    TOPOLOGY AND ITS APPLICATIONS, 2017, 222 : 77 - 99