Related papers: The link surgery modules of 2-component L-space li…
We introduce the notion of being cohomologically complete for objects of the derived category of sheaves of $Z[\hbar]$-modules on a topological space. Then we consider a $Z[\hbar]$-algebra satisfying some suitable conditions and prove…
This paper provides a new class of examples for the Koszul dualities established in~\cite{5}. We study quadratic monomial algebras from the perspective of Koszul duality, with particular emphasis on finitely presented and finitely…
We show a spectral sequence for the rational Khovanov homology of an oriented link in terms of the rational Khovanov complexes and homologies of the link surgeries along an admissible cut. As a non trivial corollary, we give an explicit…
We prove that the space of intertwining operators associated with certain admissible modules over vertex operator algebras is isomorphic to a quotient of the vector space of conformal blocks on a three-pointed rational curve defined by the…
In this paper we prove that the linear Koszul duality equivalence constructed in a previous paper provides a geometric realization of the Iwahori-Matsumoto involution of affine Hecke algebras.
When studying deformations of an $A$-module $M$, Laudal and Yau showed that one can consider 1-cocycles in the Hochschild cohomology of $A$ with coefficients in the bi-module $End_k(M).$ With this in mind, the use of higher order Hochschild…
We prove an involutive analog of the dual knot surgery formula of Eftekhary and Hedden-Levine. We also compute a small model for the local equivalence class of the involutive dual knot complex.
In this article, we generalize the concept of torsion pairs and study its structure. As a trial of obtaining all torsion pairs, we decompose torsion pairs by projective modules and injective modules. Then we calculate torsion pairs on the…
We construct a monoidal model structure on the category of all curved coalgebras and show that it is Quillen equivalent, via the extended bar-cobar adjunction, to another model structure we construct on the category of curved algebras. When…
This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $K$-theory). These dualities are expressed in terms of…
There is a well known link from the first topic in the title to the third one. In this paper we thread that link through the second topic. The central result is a criterion for the tensor nilpotence of morphisms of perfect complexes over…
Let G be a topological group such that its homology H(G) with coefficients in a principal ideal domain R is an exterior algebra, generated in odd degrees. We show that the singular cochain functor carries the duality between G-spaces and…
We define the crosscap number of a 2-component link as the minimum of the first Betti numbers of connected, non-orientable surfaces bounding the link. We discuss some properties of the crosscap numbers of 2-component links.
We explain a strategy for a proof of the positivity of all coefficients of Kazhdan-Lusztig-polynomials for arbitrary Coxeter groups by constructing spaces whose dimensions we conjecture to be these coefficients.
We give a new proof of the non-triviality of wheel graph homology classes using higher operations on Lie graph homology and a derived version of Koszul duality for modular operads.
We provide a diagrammatic computation for the bilinear form, which is defined as the pairing between the (relative) cup products with every local coefficients and every integral homology 2-class of every links in the 3-sphere. As a…
We prove the following results (1) (2) (3) on relations between $n$-links and their components. (1) Let L=(L_1, L_2) be a (4k+1)-link (4k+1\geq 5). Then we have Arf L=Arf L_1+Arf L_2. (2) Let L=(L_1, L_2) be a (4k+3)-link (4k+3\geq3). Then…
The Cyclic Surgery Theorem and Moser's work on surgeries on torus knots imply that for any non-trivial knot in $S^3$, there are at most two integer surgeries that produce a lens space. This paper investigates how many positive integer…
The aim of this short note is to present a proof of the existence of an $A_\infty$-quasi-isomorphism between the $A_\infty$-$\mathrm S(V^*)$-$\wedge(V)$-bimodule $K$, introduced in \cite{CFFR}, and the Koszul complex $\mathrm K(V)$ of…
We prove an equivariant version of the Heegaard Floer link surgery formula. As a special case, this gives an equivariant knot surgery formula for equivariant knots in $S^3$. Our proof goes by way of a naturality theorem for certain bordered…