Related papers: Universal operations in Hochschild homology
In this paper, we provide a conceptual new construction of the algebraic structure on the pair of the Hochschild cohomology spectrum (cochain complex) and Hochschild homology spectrum, which is analogous to the structure of calculus on a…
We resolve the long-standing problem of constructing the action of the operad of framed (stable) genus-$0$ curves on Hamiltonian Floer theory; this operad is equivalent to the framed $E_2$ operad. We formulate the construction in the…
We introduce the notion of $\mathrm{R}$-Eulerian sequences for any $\mathcal{N}_\infty$-ring spectrum $\mathrm{R}$ of finite orientation order. We prove that each $\mathrm{R}$-Eulerian sequence determines a stable $\mathrm{R}$-cohomology…
We obtain a decomposition for the Hochschild cochain complex of a split algebra and we study some properties of the cohomology of each term of this decomposition. Then, we consider the case of trivial extensions, specially of Frobenius…
In this paper we extend our correlation functions to the open/closed case. This gives rise to actions of an open/closed version of the Sullivan PROP as well as an action of the relevant moduli space. There are several unexpected structures…
The graph of a Hecke operator encodes all information about the action of this operator on automorphic forms over a global function field. These graphs were introduced by Lorscheid in his PhD thesis for $\text{PGL}_{2}$ and we generalized…
We consider an $A$-linear stable infinity-category $\mathcal{C}$ and the pair $(\mathcal{HH}^\bullet(\mathcal{C}/A),\mathcal{HH}_\bullet(\mathcal{C}/A))$ of the Hochschild cohomology spectrum (Hochschild cochain complex) and the Hochschild…
We analyse topological orbifold conformal field theories on the symmetric product of a complex surface M. By exploiting the mathematics literature we show that a canonical quotient of the operator ring has structure constants given by…
In two seminal papers M. Kontsevich introduced graph homology as a tool to compute the homology of three infinite dimensional Lie algebras, associated to the three operads `commutative,' `associative' and `Lie.' We generalize his theorem to…
Given a one-dimensional formal group of height 2, let E be the Morava E-theory spectrum associated to its universal deformation over the Lubin-Tate ring. By computing with moduli spaces of elliptic curves, we give an explicitation for an…
We exploit a uniform recursive procedure using preferred contractions of targets $C_*$ to construct morphisms $B_* \to C_*$ between chain complexes in a wide variety of situations. Examples include classical Alexander-Whitney and…
We define the appropriate homological setting to study deformation theory of complete locally convex (curved) dg-algebras based on Positselski's contraderived categories. We define the corresponding Hochschild complex controlling…
We give a new computation of Hochschild (co)homology of the exterior algebra, together with algebraic structures, by direct comparison with the symmetric algebra. The Hochschild cohomology is determined to be essentially the algebra of…
Given any twisting cochain t:C -->A, where C is a connected, coaugmented chain coalgebra and A is an augmented chain algebra over an arbitrary PID R, we construct a twisted extension of chain complexes A --> H(t) --> C. We show that both…
A first goal of this paper is to precisely relate the homotopy theories of bialgebras and $E_2$-algebras. For this, we construct a conservative and fully faithful $\infty$-functor from pointed conilpotent homotopy bialgebras to augmented…
We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…
We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing "algebraic" semantics for nonclassical first-order logics. This framework includes a natural notion of substitution, which allows…
In this paper, we discuss Hochschild chain models for some of the string topology operations. We use these models to simplify the proofs and computations of some of the results in string topology. Along the way we also make some new…
A modern insight due to Quillen, which is further developed by Lurie, asserts that many cohomology theories of interest are particular cases of a single construction, which allows one to define cohomology groups in an abstract setting using…
Let A be a \C-algebra with an action of a finite group G, let $\natural$ be a 2-cocycle on $G$ and consider the twisted crossed product $A \rtimes \C [G,\natural]$. We determine the Hochschild homology of $A \rtimes \C [G,\natural]$ for two…