A categorification of the Alexander polynomial in embedded contact homology
| Autor: | Gilberto Spano |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut Fourier [1973-2019] (IF [1973-2019]), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA) |
| Rok vydání: | 2017 |
| Předmět: |
Categorification
embedded contact homology Alexander polynomial 01 natural sciences Combinatorics Mathematics - Geometric Topology Knot (unit) Mathematics::Quantum Algebra [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] 0103 physical sciences FOS: Mathematics 57R58 [MATH]Mathematics [math] 0101 mathematics Mathematics::Symplectic Geometry ComputingMilieux_MISCELLANEOUS 57R17 Mathematics Conjecture 010102 general mathematics Geometric Topology (math.GT) Mathematics::Geometric Topology [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG] categorification Floer homology Mathematics - Symplectic Geometry 57M27 Symplectic Geometry (math.SG) 010307 mathematical physics Geometry and Topology |
| Zdroj: | Algebr. Geom. Topol. 17, no. 4 (2017), 2081-2124 Algebraic and Geometric Topology Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2017, 17 (4), pp.2081-2124. ⟨10.2140/agt.2017.17.2081⟩ Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2017, 17 (4), pp.2081-2124 |
| ISSN: | 1472-2739 1472-2747 2081-2124 |
| DOI: | 10.2140/agt.2017.17.2081 |
| Popis: | Given a transverse knot $K$ in a three dimensional contact manifold $(Y,\alpha)$, in [13] Colin, Ghiggini, Honda and Hutchings define a hat version of embedded contact homology for $K$, that we call $\widehat{ECK}(K,Y,\alpha)$, and conjecture that it is isomorphic to the knot Floer homology $\widehat{HFK}(K,Y)$. We define here a full version $ECK(K,Y,\alpha)$ and generalise the definitions to the case of links. We prove then that, if $Y = S^3$, $ECK$ and $\widehat{ECK}$ categorify the (multivariable) Alexander polynomial of knots and links, obtaining expressions analogue to that for knot and link Floer homologies in the plus and, respectively, hat versions. Comment: 48 pages, 4 figures |
| Databáze: | OpenAIRE |
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