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Additional gradings on generalizations of Khovanov homology and invariants of embedded surfaces.

Authors :
Manturov, Vassily Olegovich
Rushworth, William
Source :
Journal of Knot Theory & Its Ramifications. Aug2018, Vol. 27 Issue 9, pN.PAG-N.PAG. 25p.
Publication Year :
2018

Abstract

We define additional gradings on two generalizations of Khovanov homology (one due to the first author, the other due to the second), and use them to define invariants of various kinds of embeddings. These include invariants of links in thickened surfaces and of surfaces embedded in thickened 3 -manifolds. In particular, the invariants of embedded surfaces are expressed in terms of certain diagrams related to the thickened 3 -manifold, so that we refer to them as picture-valued invariants. This paper contains the first instance of such invariants for 2 -dimensional objects. The additional gradings are defined using cohomological and homotopic information of surfaces: using this information we decorate the smoothings of the standard Khovanov cube, before transferring the decorations into algebra. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
02182165
Volume :
27
Issue :
9
Database :
Academic Search Index
Journal :
Journal of Knot Theory & Its Ramifications
Publication Type :
Academic Journal
Accession number :
131486913
Full Text :
https://doi.org/10.1142/S0218216518420014