Khovanov–Lipshitz–Sarkar homotopy type for links in thickened higher genus surfaces

DOI オープンアクセス

この論文をさがす

説明

<jats:p> We discuss links in thickened surfaces. We define the Khovanov–Lipshitz–Sarkar stable homotopy type and the Steenrod square for the homotopical Khovanov homology of links in thickened surfaces with genus [Formula: see text]. A surface means a closed oriented surface unless otherwise stated. Of course, a surface may or may not be the sphere. A thickened surface means a product manifold of a surface and the interval. A link in a thickened surface (respectively, a 3-manifold) means a submanifold of a thickened surface (respectively, a 3-manifold) which is diffeomorphic to a disjoint collection of circles. Our Khovanov–Lipshitz–Sarkar stable homotopy type and our Steenrod square of links in thickened surfaces with genus [Formula: see text] are stronger than the homotopical Khovanov homology of links in thickened surfaces with genus [Formula: see text]. It is the first meaningful Khovanov–Lipshitz–Sarkar stable homotopy type of links in 3-manifolds other than the 3-sphere. We point out that our theory has a different feature in the torus case. </jats:p>

収録刊行物

詳細情報 詳細情報について

問題の指摘

ページトップへ