Geometric realization of the almost-extreme Khovanov homology of semiadequate links

被引：0

作者：

Józef H. Przytycki

Marithania Silvero

机构：

[1] Department of Mathematics at The George Washington University,

[2] University of Gdańsk,undefined

[3] Institute of Mathematics of the Polish Academy of Sciences,undefined

[4] Barcelona Graduate School of Mathematics at Universitat de Barcelona,undefined

来源：

Geometriae Dedicata | 2020年 / 204卷

关键词：

Khovanov homology; Semiadequate knot; Geometric realization; Homotopy type; Presimplicial set; 57M25; 57M27;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We recall the notion of partial presimplicial set and its geometric realization. We show that any semiadequate diagram yields a partial presimplicial set leading to a geometric realization of the almost-extreme Khovanov homology of the diagram. We give a concrete formula for the homotopy type of this geometric realization, involving wedge of spheres and a suspension of the projective plane.

引用

页码：387 / 401

页数：14

共 21 条

[1]

Eilenberg S(1950)Semi-simplicial complexes and singular homology Ann. Math. 51 499-513

[2]

Zilber J(2014)The homotopy theory of Khovanov homology Algbr. Geom. Topol. 14 2747-2781

[3]

Everitt B(2018)A geometric description of the extreme Khovanov cohomology Proc. R. Soc. Edinb. Sect. A 148 541-557

[4]

Turner P(2000)A categorification of the Jones polynomial Duke Math. J. 101 359-426

[5]

González-Meneses J(1988)Some links with nontrivial polynomials and their crossing-numbers Comment. Math. Helv. 63 527-539

[6]

Manchón PMG(2014)A Khovanov stable homotopy type J. Am. Math. Soc. 27 983-1042

[7]

Silvero M(2009)On the first group of the chromatic cohomology of graphs Geom. Dedic. 140 19-48

[8]

Khovanov M(1991)P.L. homeomorphic manifolds are equivalent by elementary shellings Eur. J. Comb. 12 129-145

[9]

Lickorish WBR(2014)Torsion in Khovanov homology of semi-adequate links Fund. Math. 225 277-303

[10]

Thistlethwaite MB(2018)Homotopy type of circle graphs complexes motivated by extreme Khovanov homology J. Algebraic Comb. 48 119-156

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