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A categorification of the skein module of tangles | | Marta M. Asaeda
; Jozef H. Przytycki
; Adam S. Sikora
; | | Date: |
9 Oct 2004 | | Subject: | Quantum Algebra; Geometric Topology MSC-class: 57M27 | math.QA math.GT | | Abstract: | We define new homology groups of tangles which are invariant under isotopies and prove that they categorify the Kauffman bracket skein module of tangles. Our homology of 0-tangles coincides (up to normalization) with Khovanov link homology. Our homology of 1-tangles has an interpretation in terms of the reduced Khovanov homology. For any tangle T_3 composed of tangles T_1 and T_2 we define a spectral sequence converging to the homology of T_3 whose second term is composed of homologies of T_1 and T_2. | | Source: | arXiv, math.QA/0410238 | | Services: | Forum | Review | PDF | Favorites | |
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