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Volume 32, Issue 3
A Formula for Khovanov Type Link Homology of Pretzel Knots

Meili Zhang, Fengchun Lei, Fengling Li & Dongxu Wang

DOI: 10.13447/j.1674-5647.2016.03.02

Commun. Math. Res., 32 (2016), pp. 198-206.

Published online: 2021-05

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  • Abstract

Khovanov type homology is a generalization of Khovanov homology. The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots $P(−n, −m, m)$. The computations reveal that the rank of the homology of pretzel knots is an invariant of $n$. The proof is based on a "shortcut" and two lemmas that recursively reduce the computational complexity of Khovanov type homology.

  • Keywords

pretzel knot, Khovanov type homology, Frobenius algebra, TQFT.

  • AMS Subject Headings

57M25, 57M27, 16W30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-32-198, author = {Zhang , MeiliLei , FengchunLi , Fengling and Wang , Dongxu}, title = {A Formula for Khovanov Type Link Homology of Pretzel Knots}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {32}, number = {3}, pages = {198--206}, abstract = {

Khovanov type homology is a generalization of Khovanov homology. The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots $P(−n, −m, m)$. The computations reveal that the rank of the homology of pretzel knots is an invariant of $n$. The proof is based on a "shortcut" and two lemmas that recursively reduce the computational complexity of Khovanov type homology.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2016.03.02}, url = {http://global-sci.org/intro/article_detail/cmr/18898.html} }
TY - JOUR T1 - A Formula for Khovanov Type Link Homology of Pretzel Knots AU - Zhang , Meili AU - Lei , Fengchun AU - Li , Fengling AU - Wang , Dongxu JO - Communications in Mathematical Research VL - 3 SP - 198 EP - 206 PY - 2021 DA - 2021/05 SN - 32 DO - http://doi.org/10.13447/j.1674-5647.2016.03.02 UR - https://global-sci.org/intro/article_detail/cmr/18898.html KW - pretzel knot, Khovanov type homology, Frobenius algebra, TQFT. AB -

Khovanov type homology is a generalization of Khovanov homology. The main result of this paper is to give a recursive formula for Khovanov type homology of pretzel knots $P(−n, −m, m)$. The computations reveal that the rank of the homology of pretzel knots is an invariant of $n$. The proof is based on a "shortcut" and two lemmas that recursively reduce the computational complexity of Khovanov type homology.

Meili Zhang, Fengchun Lei, Fengling Li & Dongxu Wang. (2021). A Formula for Khovanov Type Link Homology of Pretzel Knots. Communications in Mathematical Research . 32 (3). 198-206. doi:10.13447/j.1674-5647.2016.03.02
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