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
  • [41] Torsion in thin regions of Khovanov homology
    Chandler, Alex
    Lowrance, Adam M.
    Sazdanovic, Radmila
    Summers, Victor
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2022, 74 (03): : 630 - 654
  • [42] Khovanov homology, Lee homology and a Rasmussen invariant for virtual knots
    Dye, Heather A.
    Kaestner, Aaron
    Kauffman, Louis H.
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2017, 26 (03)
  • [43] Annular Khovanov homology and meridional disks
    Martin, Gage
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2023, 32 (02)
  • [44] Remarks on Khovanov Homology and the Potts Model
    Kauffman, Louis H.
    PERSPECTIVES IN ANALYSIS, GEOMETRY, AND TOPOLOGY: ON THE OCCASION OF THE 60TH BIRTHDAY OF OLEG VIRO, 2012, 296 : 237 - 262
  • [45] Surgery obstructions from Khovanov homology
    Liam Watson
    Selecta Mathematica, 2012, 18 : 417 - 472
  • [46] Khovanov homology is an unknot-detector
    P. B. Kronheimer
    T. S. Mrowka
    Publications mathématiques de l'IHÉS, 2011, 113 : 97 - 208
  • [47] Khovanov homology and categorification of skein modules
    Queffelec, Hoel
    Wedrich, Paul
    QUANTUM TOPOLOGY, 2021, 12 (01) : 129 - 209
  • [49] Virtual Khovanov homology using cobordisms
    Tubbenhauer, Daniel
    JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 2014, 23 (09)
  • [50] Khovanov-Kauffman homology for embedded graphs
    Al-Yasry, Ahmad Zainy
    RIVISTA DI MATEMATICA DELLA UNIVERSITA DI PARMA, 2014, 5 (02): : 435 - 442