Skein lasagna modules and handle decompositions
نویسندگان
چکیده
The skein lasagna module is an extension of Khovanov–Rozansky homology to the setting a four-manifold and link in its boundary. This invariant plays role Hilbert space associated fully extended (4+ϵ)-dimensional TQFT. We give general procedure for expressing terms handle decomposition four-manifold. use this calculate few examples, show that can sometimes be locally infinite dimensional.
منابع مشابه
On the Kauffman Skein Modules
Abstract. Let k be a subring of the field of rational functions in α, s which contains α, s. Let M be a compact oriented 3-manifold, and let K(M) denote the Kauffman skein module of M over k. Then K(M) is the free k-module generated by isotopy classes of framed links in M modulo the Kauffman skein relations. In the case of k = Q(α, s), the field of rational functions in α, s, we give a basis fo...
متن کاملSkein Modules of 3-manifolds
It is natural to try to place the new polynomial invariants of links in algebraic topology (e.g. to try to interpret them using homology or homotopy groups). However, one can think that these new polynomial invariants are byproducts of a new more delicate algebraic invariant of 3-manifolds which measures the obstruction to isotopy of links (which are homotopic). We propose such an algebraic inv...
متن کاملOn Constructions of Generalized Skein Modules
Jozef Przytycki introduced skein modules of 3-manifolds and skein deformation initiating algebraic topology based on knots. We discuss the generalized skein modules of Walker, defined by fields and local relations. Some results by Przytycki are proven in a more general setting of fields defined by decorated cell-complexes in manifolds. A construction of skein theory from embedded TQFT-functors ...
متن کاملFundamentals of Kauffman bracket skein modules
Skein modules are the main objects of an algebraic topology based on knots (or position). In the same spirit as Leibniz we would call our approach algebra situs. When looking at the panorama of skein modules1, we see, past the rolling hills of homologies and homotopies, distant mountains the Kauffman bracket skein module, and farther off in the distance skein modules based on other quantum inva...
متن کاملDecompositions of Modules and Comodules
It is well-known that any semiperfect A ring has a decomposition as a direct sum (product) of indecomposable subrings A = A1 ⊕ · · · ⊕ An such that the Ai-Mod are indecomposable module categories. Similarly any coalgebra C over a field can be written as a direct sum of indecomposable subcoalgebras C = ⊕ I Ci such that the categories of Ci-comodules are indecomposable. In this paper a decomposit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2023
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2023.109071