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霍万诺夫同伦型、周期链环与局部化

Khovanov homotopy type, periodic links and localizations.

作者信息

Borodzik Maciej, Politarczyk Wojciech, Silvero Marithania

机构信息

Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland.

Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland.

出版信息

Math Ann. 2021;380(3-4):1233-1309. doi: 10.1007/s00208-021-02157-y. Epub 2021 Feb 19.

DOI:10.1007/s00208-021-02157-y
PMID:34776536
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8550572/
Abstract

Given an -periodic link , we show that the Khovanov spectrum constructed by Lipshitz and Sarkar admits a group action. We relate the Borel cohomology of to the equivariant Khovanov homology of constructed by the second author. The action of Steenrod algebra on the cohomology of gives an extra structure of the periodic link. Another consequence of our construction is an alternative proof of the localization formula for Khovanov homology, obtained first by Stoffregen and Zhang. By applying the Dwyer-Wilkerson theorem we express Khovanov homology of the quotient link in terms of equivariant Khovanov homology of the original link.

摘要

给定一个(n)周期链环(L)，我们证明由利普希茨和萨卡尔构建的霍万诺夫谱允许一个群作用。我们将(L)的博雷尔上同调与第二作者构建的(L)的等变霍万诺夫同调联系起来。斯廷罗德代数在(L)的上同调上的作用给出了周期链环的一个额外结构。我们构造的另一个结果是对霍万诺夫同调局部化公式的另一种证明，该公式最初由斯托夫雷根和张得到。通过应用德怀尔 - 威尔克森定理，我们用原始链环的等变霍万诺夫同调来表示商链环的霍万诺夫同调。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/f943253a249d/208_2021_2157_Fig16_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/f943253a249d/208_2021_2157_Fig16_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/b5914874ae84/208_2021_2157_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/79214b0439c3/208_2021_2157_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/a8e05f91b83e/208_2021_2157_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/95bd6a72c482/208_2021_2157_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/d5d239a733d3/208_2021_2157_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/ed9a619af7be/208_2021_2157_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/4868d19c06ec/208_2021_2157_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/94e245f144d3/208_2021_2157_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/c3aeb12adbe0/208_2021_2157_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/3479531d37d1/208_2021_2157_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/48cfd92bc91d/208_2021_2157_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/911462f79364/208_2021_2157_Fig12_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/064228e7c869/208_2021_2157_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/e99c1882168d/208_2021_2157_Fig14_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/9ac4b08c0e3b/208_2021_2157_Fig15_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/a7ae/8550572/f943253a249d/208_2021_2157_Fig16_HTML.jpg

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