Tangle Floer homology and cobordisms between tangles
| Autor: | Eaman Eftekhary, Akram Alishahi |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Functor 010102 general mathematics Geometric topology Cobordism Geometric Topology (math.GT) 01 natural sciences Mathematics::Algebraic Topology Mathematics::Geometric Topology Tangle Mathematics - Geometric Topology Morphism Floer homology Mathematics::K-Theory and Homology Mathematics::Quantum Algebra 0103 physical sciences FOS: Mathematics 010307 mathematical physics Geometry and Topology 0101 mathematics Commutative algebra Link (knot theory) Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Journal of Topology |
| Popis: | We introduce a generalization of oriented tangles, which are still called tangles, so that they are in one-to-one correspondence with the sutured manifolds. We define cobordisms between sutured manifolds (tangles) by generalizing cobordisms between oriented tangles. For every commutative algebra A over Z/2Z, we define A-Tangles to be the category consisting of A-tangles, which are balanced tangles with A-colorings of the tangle strands and fixed SpinC structures, and A-cobordisms as morphisms. An A-cobordism is a cobordism with a compatible A-coloring and an affine set of SpinC structures. Associated with every A-module M we construct a functor $HF^M$ from A-Tangles to A-Modules, called the tangle Floer homology functor, where A-Modules denotes the the category of A-modules and A-homomorphisms between them. Moreover, for any A-tangle T the A-module $HF^M(T)$ is the extension of sutured Floer homology defined in an earlier work of the authors. In particular, this construction generalizes the 4-manifold invariants of Ozsvath and Szabo. Moreover, applying the above machinery to decorated cobordisms between links, we get functorial maps on link Floer homology. Comment: 66 pages, Corrected Typos, Section 8.3 is moved to a new paper: arXiv:1810.05125 |
| Databáze: | OpenAIRE |
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