霍瓦诺夫同源性检测分裂链接

IF 1.7 1区数学 Q1 MATHEMATICS

American Journal of Mathematics Pub Date : 2019-10-09 DOI:10.1353/ajm.2022.0043

Robert Lipshitz, Sucharit Sarkar

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引用次数: 2

摘要

扩展了Hedden-Ni的思想，证明了Khovanov同构上的模结构可以检测分离链路。我们还证明了分枝重盖的未扭曲Heegaard花同源性的一个类似物。在此过程中所证明的技术成果包括:用扭转Heegaard Floer同构对非扭Heegaard Floer同构上的模结构的两种解释，以及连杆的约化Khovanov复上的模结构被很好地定义到拟同构。

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Khovanov homology detects split links

abstract:Extending ideas of Hedden-Ni, we show that the module structure on Khovanov homology detects split links. We also prove an analogue for untwisted Heegaard Floer homology of the branched double cover. Technical results proved along the way include two interpretations of the module structure on untwisted Heegaard Floer homology in terms of twisted Heegaard Floer homology and the fact that the module structure on the reduced Khovanov complex of a link is well defined up to quasi-isomorphism.

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来源期刊

American Journal of Mathematics 数学-数学

CiteScore

3.20

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： The oldest mathematics journal in the Western Hemisphere in continuous publication, the American Journal of Mathematics ranks as one of the most respected and celebrated journals in its field. Published since 1878, the Journal has earned its reputation by presenting pioneering mathematical papers. It does not specialize, but instead publishes articles of broad appeal covering the major areas of contemporary mathematics. The American Journal of Mathematics is used as a basic reference work in academic libraries, both in the United States and abroad.