Related papers: Some remarks on Dupont contraction
The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…
Given a symplectic form and a pseudo-riemannian metric on a manifold, a non degenerate even Poisson bracket on the algebra of differential forms is defined and its properties are studied. A comparison with the Koszul-Schouten bracket is…
Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of…
We show that any closed model category of simplicial algebras over an algebraic theory is Quillen equivalent to a proper closed model category. By ``simplicial algebra'' we mean any category of algebras over a simplicial algebraic theory,…
We introduce a notion of join for (augmented) simplicial sets generalising the classical join of geometric simplicial complexes. The definition comes naturally from the ordinal sum on the base simplicial category $\Delta$.
Defined by a single axiom, finite abstract simplicial complexes belong to the simplest constructs of mathematics. We look at a a few theorems.
We introduce a notion of discrete topological complexity in the setting of simplicial complexes, using only the combinatorial structure of the complex by means of the concept of contiguous simplicial maps. We study the links of this new…
The class of simplicial complexes representing triangulations and subdivisions of Lawrence polytopes is closed under Alexander duality. This gives a new geometric model for oriented matroid duality.
We investigate the space of simplices in Euclidean Space
This paper extends the results of "Operads and Algebraic Homotopy" in giving algebraic invariants for the stable homotopy type of a pointed simply-connected simplicial set.
Discrete normal surfaces are normal surfaces whose intersection with each tetrahedron of a triangulation has at most one component. They are also natural Poincar\'e duals to 1-cocycles with $\ZZ/2\ZZ$-coefficients. For a fixed cohomology…
The spaces of flattenings of a simplicial sphere played a key role in the study of existence and uniqueness of differentiable structures on a simplicial sphere. In this paper, we will establish that the spaces of flattenings of some…
We provide necessary and sufficient conditions for simplicial complexes whose determinantal facet ideals admit reduced Grobner bases under diagonal term orders. Building on and extending foundational results for binomial edge ideals and…
The simplicial extension of any functor from Sets to Sets which commutes with directed colimits takes weak equivalences to weak equivalences. The goal of the present paper is construct a framework which can be used to proof results of this…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
We investigate simpliciality of function spaces without constants. We prove, in particular, that several properties characterizing simpliciality in the classical case differ in this new setting. We also show that it may happen that a given…
In this paper, we generalize some of the results of [9], and add some new results. Furthermore, we take a closer look at strongly simple algebras, which are introduced in [9].
We present a theory of reduction for Courant algebroids as well as Dirac structures, generalized complex, and generalized K\"ahler structures which interpolates between holomorphic reduction of complex manifolds and symplectic reduction.…
By the famous ADE classification rational double points are simple. Rational triple points are also simple. We conjecture that the simple normal surface singularities are exactly those rational singularities, whose resolution graph can be…
A theory of cotetrad fields on a four-dimensional manifold is considered. Its configuration space coincides with that of the Teleparallel Equivalent of General Relativity but its dynamics is much simpler. We carry out the Legendre…