Khovanov homology and the slice genus

被引：0

作者：

Jacob Rasmussen

机构：

[1] Princeton University,Dept. of Mathematics

[2] University of Cambridge,DPMMS

来源：

Inventiones mathematicae | 2010年 / 182卷

关键词：

Spectral Sequence; Short Exact Sequence; Jones Polynomial; Planar Diagram; Floer Homology;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We use Lee’s work on the Khovanov homology to define a knot invariant s. We show that s(K) is a concordance invariant and that it provides a lower bound for the smooth slice genus of K. As a corollary, we give a purely combinatorial proof of the Milnor conjecture.

引用

页码：419 / 447

页数：28

共 50 条

[1] Khovanov homology and the slice genus
Rasmussen, Jacob
INVENTIONES MATHEMATICAE, 2010, 182 (02) : 419 - 447
[2] A slice genus lower bound from sl(n) Khovanov-Rozansky homology
Lobb, Andrew
ADVANCES IN MATHEMATICS, 2009, 222 (04) : 1220 - 1276
[3] Extremal Khovanov homology of Turaev genus one links
Dasbach, Oliver T.
Lowrance, Adam M.
FUNDAMENTA MATHEMATICAE, 2020, 250 (01) : 63 - 99
[4] Near extremal Khovanov homology of Turaev genus one links
Beldon, Theo
Destefano, Mia
Lowrance, Adam M.
Milgrim, Wyatt
Villasenor, Cecilia
TOPOLOGY AND ITS APPLICATIONS, 2024, 346
[5] Unoriented Khovanov Homology
Baldridge, Scott
Kauffman, Louis H.
McCarty, Ben
NEW YORK JOURNAL OF MATHEMATICS, 2022, 28 : 367 - 401
[6] NOT EVEN KHOVANOV HOMOLOGY
Vaz, Pedro
PACIFIC JOURNAL OF MATHEMATICS, 2020, 308 (01) : 223 - 256
[7] Localization in Khovanov homology
Stoffregen, Matthew
Zhang, Melissa
GEOMETRY & TOPOLOGY, 2024, 28 (04)
[8] An Introduction to Khovanov Homology
Kauffman, Louis H.
KNOT THEORY AND ITS APPLICATIONS, 2016, 670 : 105 - 139
[9] Torsion of Khovanov homology
Shumakovitch, Alexander N.
FUNDAMENTA MATHEMATICAE, 2014, 225 : 343 - 364
[10] Rotors in Khovanov Homology
MacColl, Joseph
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2016, 59 (01): : 159 - 169

← 1 2 3 4 5 →