Related papers: Brane actions for coherent $\infty$-operads

The purpose of this paper is twofold. First, we review applications of the bar duality of operads to the construction of explicit cofibrant replacements in categories of algebras over an operad. In view toward applications, we check that…

Numerably contractible spaces play an important role in the theory of homotopy pushouts and pullbacks. The corresponding results imply that a number of well known weak homotopy equivalences are genuine ones if numerably contractible spaces…

A kappa-symmetric action for coincident D-branes is presented. It is valid in the approximation that the additional fermionic variables, used to incorporate the non-abelian degrees of freedom, are treated classically. The action is written…

We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra…

We show that a profinite completion functor for (simplicial or topological) operads with good homotopical properties can be constructed as a left Quillen functor from an appropriate model category of infinity-operads to a certain model…

We derive the complete $(curvature)^2$ terms of effective D-brane actions, for arbitrary ambient geometries and world-volume embeddings, at lowest order (disk-level) in the string-loop expansion. These terms reproduce the $o(\alpha'^2)$…

It is shown that every algebra over the chain operad of the little disks operad gives naturally rise to a Hertling-Manin's F-manifold, that is a smooth manifold equipped with an integrable graded commutative associative product on the…

Hurwitz spaces are homotopy quotients of the braid group action on the moduli space of principal bundles over a punctured plane. By considering a certain model for this homotopy quotient we build an aspherical topological operad that we…

We subject the phenomenologically successful large volume scenario of hep-th/0502058 to a first consistency check in string theory. In particular, we consider whether the expansion of the string effective action is consistent in the…

Coherent unit actions on a binary, quadratic operad were introduced by Loday and were shown by him to give Hopf algebra structures on the free algebras when the operad is also regular with a splitting of associativity. Working with such…

For a real oriented hyperplane arrangement, we show that the corresponding Salvetti complex is homotopy equivalent to the complement of the complexified arrangement. This result was originally proved by M. Salvetti. Our proof follows the…

Suppose $G$ is a finite group. In this paper, we construct an equivalence between the $\infty$-category of algebras over an $N_{\infty}$-operad $\mathcal{O}$ associated to a $G$-indexing system $\mathcal{I}$ and the corresponding…

We extend the notion of effective resistance to metric spaces that are similar to graphs but can also be similar to fractals. Combined with other basic facts proved in the paper, this lays the ground for a construction of Brownian Motion on…

Let $G_\Gamma\curvearrowright X$ and $G_\Lambda\curvearrowright Y$ be two free measure-preserving actions of one-ended right-angled Artin groups with trivial center on standard probability spaces. Assume they are irreducible, i.e. every…

We obtain actions for N D-branes occupying points in a manifold with arbitrary Kahler metric. In one complex dimension, the action is uniquely determined (up to second order in commutators) by the requirement that it reproduce the masses of…

The modular envelope of a cyclic operad is the smallest modular operad containing it. A modular operad is constructed from moduli spaces of Riemann surfaces with boundary; this modular operad is shown to be the modular envelope of the…

We prove that the homotopy theory of $N_\infty$ operads is equivalent to a homotopy theory of discrete operads, and we construct free and associative operadic realizations of every indexing system. This resolves a conjecture of Blumberg and…

We show that Lurie's model for $\infty$-operads (or more precisely a "flagged" or "pinned" version thereof) is equivalent to the analytic monads previously studied by Gepner, Kock, and the author, with an $\infty$-operad $\mathcal{O}$…

We show that relative loop spaces are recognized by $A_\infty$-actions. A certain version of the 2-sided bar construction is used to prove such recognition theorem. The operad ${\sf Act}_\infty$ of $A_\infty$-actions is presented in terms…

In this paper we extend our previous results on wrapping Brownian motion and heat kernels onto compact Lie groups to various symmetric spaces, where a global generalisation of Rouvi\`ere's formula and the $e$-function are considered.…