Patterns in odd Khovanov homology
| Autor: | Alexander N. Shumakovitch |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2011 |
| Předmět: |
Khovanov homology
Algebra and Number Theory 010102 general mathematics Geometric Topology (math.GT) Mathematics::Algebraic Topology 01 natural sciences Mathematics::Geometric Topology Knot theory Combinatorics Mathematics - Geometric Topology Mathematics::K-Theory and Homology Mathematics - Symplectic Geometry Mathematics::Quantum Algebra 0103 physical sciences Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) Symplectic Geometry (math.SG) 010307 mathematical physics Thurston–Bennequin number 0101 mathematics Mathematics::Symplectic Geometry Topology (chemistry) Mathematics |
| Popis: | We investigate properties of the odd Khovanov homology, compare and contrast them with those of the original (even) Khovanov homology, and discuss applications of the odd Khovanov homology to other areas of knot theory and low-dimensional topology. We show that it provides an effective upper bound on the Thurston-Bennequin number of Legendrian links and can be used to detect quasi-alternating knots. A potential application to detecting transversely non-simple knots is also mentioned. 17 pages, 12 figures; v.3: Journal reference is added, references are updated |
| Databáze: | OpenAIRE |
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