Related papers: The inverse function theorem for curved L-infinity…

In this paper we prove a local surjection theorem with continuous right-inverse for maps between Banach spaces, and we apply it to a class of inversion problems with loss of derivatives.

We construct counterexamples to classical calculus facts such as the Inverse and Implicit Function Theorems in Scale Calculus -- a generalization of Multivariable Calculus to infinite dimensional vector spaces in which the…

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…

Let $S$ be a compact oriented surface. We construct homogeneous quasimorphisms on $Diff(S, area)$, on $Diff_0(S, area)$ and on $Ham(S)$ generalizing the constructions of Gambaudo-Ghys and Polterovich. We prove that there are infinitely many…

Let X be a smooth complex projective variety, and let Y in X be a smooth very ample hypersurface such that -K_Y is nef. Using the technique of relative Gromov-Witten invariants, we give a new short and geometric proof of (a version of) the…

We study cohomology theories of strongly homotopy algebras, namely $A_\infty, C_\infty$ and $L_\infty$-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of $C_\infty$-algebras thus generalising previous work…

By means of $C^\infty$-connections we will prove a general second main theorem and some special ones for holomorphic curves. The method gives a geometric proof of H. Cartan's second main theorem in 1933. By applying the same method, we will…

We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers. In particular, we prove the homotopy…

In this paper, we aim to provide a notion of "relative objects", i.e. objects equipped with some sort of subobjects, in differential topology. In spite of active researches relating them, e.g. knot theory or the theory of manifolds with…

The notion of a derived A-infinity algebra, considered by Sagave, is a generalization of the classical notion of A-infinity algebra, relevant to the case where one works over a commutative ring rather than a field. We initiate a study of…

Given a topological group G, its orbit category Orb_G has the transitive G-spaces G/H as objects and the G-equivariant maps between them as morphisms. A well known theorem of Elmendorf then states that the category of G-spaces and the…

We show that a fairly arbitrary Frechet space topology on the space of holomorphic functions on a domain controls the topology of uniform convergence on compact sets. In fact it turns out that the result we present can be proved more simply…

In this paper we develop the $A_\infty$-analog of the Maurer-Cartan simplicial set associated to an $L_\infty$-algebra and show how we can use this to study the deformation theory of $\infty$-morphisms of algebras over non-symmetric…

The dihedral homology functor $HD:A_\infty^{{\rm inv}}(K)\to GrM(K)$ from the category $A_\infty^{{\rm inv}}(K)$ of involutive $A_\infty$-algebras over any commutative unital ring $K$ to the category $GrM(K)$ of graded $K$-modules is…

Let $(M,g)$ be an incomplete Riemannian manifold of finite volume and let $2\leq p<\infty$. In the first part of this paper we prove that under certain assumptions the inclusion of the space of $L^p$-differential forms into that of…

Let $\left(\mathcal{H},\left(.,.\right)\right)$ be a Hilbert space and let $\mathcal{L}\left(\mathcal{H}\right)$ be the linear space of bounded operators in $\mathcal{H}$. In this paper, we deal with $\mathcal{L}(\mathcal{H})$-valued…

In this article, we give an explicit description of the invertible functions on the Drinfeld symmetric space over $K$ a finite extension of $\mathbb{Q}_p$. We identify them with some distribution spaces over the profinite set of…

This is an addendum to the paper ``Deformation of $L_\infty$-Algebras'' of the same author. We explain in which way the deformation theory of $L_\infty$-algebras extends the deformation theory of singularities. We show that the construction…

In this paper, we obtain the reversed Hardy-Littlewood-Sobolev inequality with vertical weights on the upper half space and discuss the extremal functions. We show that the sharp constants in this inequality are attained by introducing a…

We give a construction of the universal enveloping $A_\infty$ algebra of a given $L_\infty$ algebra, alternative to the already existing versions. As applications, we derive a higher homotopy algebras version of the classical Milnor-Moore…