论文标题
Khovanov同源性的Kirby颜色
A Kirby color for Khovanov homology
论文作者
论文摘要
我们在Khovanov同源性的环境中构建了Kirby颜色：Annular Bar-Natan类别的索引，配备了自然手柄幻灯片同构。使用Khovanov同源性的功能性和电缆特性，我们定义了一个Kirby色的Khovanov同源性，该同源物在手柄幻灯片下移动下不变，直至同构。通过Manolescu-Neithalath 2 Handle公式，Kirby色的Khovanov同源性与$ \ Mathfrak {gl} _ {2} $ Skein Lasagna模块一致，因此是$ 4 $ dimeciperional $ 2 $ 2 $ handlebodies的不变性。
We construct a Kirby color in the setting of Khovanov homology: an ind-object of the annular Bar-Natan category that is equipped with a natural handle slide isomorphism. Using functoriality and cabling properties of Khovanov homology, we define a Kirby-colored Khovanov homology that is invariant under the handle slide Kirby move, up to isomorphism. Via the Manolescu--Neithalath 2-handle formula, Kirby-colored Khovanov homology agrees with the $\mathfrak{gl}_{2}$ skein lasagna module, hence is an invariant of $4$-dimensional $2$-handlebodies.
