Related papers: Twisted Bar Construction
The covariant descripion is constructed for the Wick-type symbols on symplectic manifolds by means of the Fedosov procedure. The geometry of the manifolds admitting this symbol is explored. The superextended version of the Wick-type…
We give a complete proof of the twisted duality property M(q)'= Z M(q^\perp) Z* of the (self-dual) CAR-Algebra in any Fock representation. The proof is based on the natural Halmos decomposition of the (reference) Hilbert space when two…
In this paper, we present a unified framework for studying cohomology theories of various operators in the context of pseudoalgebras. The central tool in our approach is the notion of a quasi-twilled Lie pseudoalgebra. We introduce two…
In this paper, we study the perturbative aspects of the half-twisted variant of Witten's topological A-model coupled to a non-dynamical gauge field with Kahler target space X being a G-manifold. Our main objective is to furnish a purely…
Tied links and the tied braid monoid were introduced recently by the authors and used to define new invariants for classical links. Here, we give a version purely algebraic-combinatoric of tied links. With this new version we prove that the…
Let $X$ be a quasi-projective curve, compactified to $(Y,D)$ with $X=Y-D$. We construct a Deligne-Hitchin twistor space out of moduli spaces of framed $\lambda$-connections of rank $2$ over $Y$ with logarithmic singularities and…
The twisted torsion of a 3-manifold is well-known to be zero whenever the corresponding twisted Alexander module is non-torsion. Under mild extra assumptions we introduce a new twisted torsion invariant which is always non-zero. We show how…
Toric orbifolds are a topological generalization of projective toric varieties associated to simplicial fans. We introduce some sufficient conditions on the combinatorial data associated to a toric orbifold to ensure the existence of an…
Twisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is dis- cussed in the case when X is a product of a circle T and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral…
In this paper we make an attempt to study right loops $(S, o)$ in which, for each $y\in S$, the map $\sigma_y$ from the inner mapping group $G_S$ of $(S, o)$ to itself given by $\sigma_y (h)(x) o\ h(y)= h(xoy)$, $x\in S, h\in G_S$ is a…
We define an invariant $\nabla_G(M)$ of pairs M,G, where M is a 3-manifold obtained by surgery on some framed link in the cylinder $S\times I$, S is a connected surface with at least one boundary component, and G is a fatgraph spine of S.…
We study open books (or open book decompositions) of a closed oriented 3-manifold which support overtwisted contact structures. We focus on a simple closed curve along which one can perform Stallings twist, called ``twisting loop''. We show…
In earlier work of two of the authors, two 1-loop polynomial invariants of cusped 3-manifolds were constructed using combinatorial data of ideal triangulations, and conjectured to be equal to the $\mathbb{C}^2$ and the…
Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…
The purpose of this paper is to introduce the cohomology and deformations of twisted Rota-Baxter operators on 3-Leibniz algebras and NS-3-Leibniz algebras. We construct an $L_\infty$-algebra whose Maurer-Cartan elements are twisted…
We introduce the $\mathcal{T}$-construction, an endofunctor on the category of generalized operads as a general mechanism by which various notions of plethystic substitution arise from more ordinary notions of substitution. In the special…
Homotopy type theory is a logical setting based on Martin-L\"of type theory in which geometric constructions and proofs can be carried out synthetically. Here, types can be interpreted as spaces up to homotopy, and proofs as…
Recently, at least 50 million of novel examples of compact $G_2$ holonomy manifolds have been constructed as twisted connected sums of asymptotically cylindrical Calabi-Yau threefolds. The purpose of this paper is to study mirror symmetry…
Carlsson's construction is a simplicial group whose geometric realization is the loop space of the 1-stunted reduced Borel construction. Our main results are: i) Given a pointed simplicial set acted upon by the discrete cyclic group C_2 of…
We generalize unoriented handlebody-links to the twisted virtual case, obtaining Reidemeister moves for handlebody-links in ambient spaces of the form $\Sigma\times [0,1]$ for $\Sigma$ a compact closed 2-manifold up to stable equivalence.…