Related papers: The derived Maurer-Cartan locus

Over a field of characteristic zero, we show that the forgetful functor from the homotopy category of commutative dg algebras to the homotopy category of dg associative algebras is faithful. In fact, the induced map of derived mapping…

Locally cartesian closed (lcc) categories are natural categorical models of extensional dependent type theory. This paper introduces the "gros" semantics in the category of lcc categories: Instead of constructing an interpretation in a…

We explicitly describe the Lie algebras $M_L$ of ladder matrices in $M_n$ associate with dominant upper triangular ladders $L$, and completely characterize the derivations of these $M_L$ over a field $F$ with $char(F) \neq 2$. We also…

Berwick-Evens and Lerman recently showed that the category of vector fields on a geometric stack has the structure of a Lie $2$-algebra. Motivated by this work, we present a construction of graded weak Lie $2$-algebras associated with…

Let M be a complete Riemannian manifold, D a Dirac-type operator on M whose Weitzenbock curvature is uniformly positive on the complement of a subset Z of M. We show that the coarse index of D is localized to the K-theory of the coarse…

We prove that the partial derivative of the volume function of big classes along any real divisor in a compact Kaehler manifold is equal to the numerical restricted volume of that class to the divisor. A consequence of our main result is…

I consider differential of mapping $f$ of continuous division ring as linear mapping the most close to mapping $f$. Different expressions which correspond to known deffinition of derivative are supplementary. I explore the Gateaux…

We construct a monoidal version of Lurie's un/straightening equivalence. In more detail, for any symmetric monoidal $\infty$-category $\mathbf C$, we endow the $\infty$-category of coCartesian fibrations over $\mathbf C$ with a (naturally…

We construct a symmetric monoidal category $LIE^{MC}$ whose objects are shifted L-infinity algebras equipped with a complete descending filtration. Morphisms of this category are "enhanced" infinity morphisms between shifted L-infinity…

This document is a reorganization of the results on the Master Thesis of the same title written by the author under the supervision of Dr. Christian Blohmann at the University of Bonn in 2014. There are three main results in this document.…

Given a finite type degree-wise nilpotent $L_\infty$-algebra, we construct an abelian group that acts on the set of Maurer-Cartan elements of the given $L_\infty$-algebra so that the quotient by this action becomes the moduli space of…

We consider finite approximations of a topological space $M$ by noncommutative lattices of points. These lattices are structure spaces of noncommutative $C^*$-algebras which in turn approximate the algebra $\cc(M)$ of continuous functions…

We introduce a notion of coisotropics on 1-shifted symplectic Lie groupoids (i.e. quasi-symplectic groupoids) using twisted Dirac structures and show that it satisfies properties analogous to the corresponding derived-algebraic notion in…

Theory of differential operators on associative algebras is not extended to the non-associative ones in a straightforward way. We consider differential operators on Lie algebras. A key point is that multiplication in a Lie algebra is its…

The classical transversality lemma of contact geometry constructs a contact structure on a hypersurface transverse to a Liouville vector field using point-set topology and local flows. This paper translates the classical transversality…

The deformation theory of a Dirac structure is controlled by a differential graded Lie algebra which depends on the choice of an auxiliary transversal Dirac structure; if the transversal is not involutive, one obtains an $L_\infty$ algebra…

This paper is devoted to the comparison of different localized categories of differential complexes. The first result is that the canonical functor from the category of complexes of differential operators of order one (defined by Herrera…

The purpose of this memoir is to study pre-Lie algebras up to homotopy with divided powers, and to use this algebraic structure for the study of mapping spaces in the category of operads. We define a new notion of algebra called…

A graded poset structure is defined for the sets of Littlewood-Richardson (LR) tableaux that count the multiplicity of an irreducible GL(n)-module in the tensor product of irreducibles indexed by a sequence of rectangular partitions. This…

We analyze a model for the homotopy theory of complete filtered $L_\infty$-algebras intended for applications in algebraic and algebro-geometric deformation theory. We provide an explicit proof of an unpublished result of E.\ Getzler which…