On a triply graded Khovanov homology
| Autor: | Krzysztof K. Putyra |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Khovanov homology
Pure mathematics Algebra and Number Theory 010102 general mathematics Multiplicative function Geometric Topology (math.GT) 02 engineering and technology Disjoint sets Homology (mathematics) 01 natural sciences Connected sum 55N35 57M27 Mathematics - Geometric Topology 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Algebraic Topology (math.AT) 020201 artificial intelligence & image processing Mathematics - Algebraic Topology 0101 mathematics Invariant (mathematics) Mathematics |
| Popis: | Cobordisms are naturally bigraded and we show that this grading extends to Khovanov homology, making it a triply graded theory. Although the new grading does not make the homology a stronger invariant, it can be used to show that odd Khovanov homology is multiplicative with respect to disjoint unions and connected sums of links; same results hold for the generalized Khovanov homology defined by the author in his previous work. We also examine the module structure on both odd and even Khovanov homology, in particular computing the effect of sliding a basepoint through a crossing on the integral homology. 21 pages. Some diagrams use colors, but they are readable when printed black and white |
| Databáze: | OpenAIRE |
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