Related papers: Manifold calculus adapted for simplicial complexes
We study functors F from C_f to D where C and D are simplicial model categories and C_f is the full subcategory of C consisting of objects that factor a fixed morphism f from A to B. We define the analogs of Eilenberg and Mac Lane's cross…
We study a variant of the embedding functor $\mathop{\mathrm{Emb}}(M, N)$ that incorporates homotopical data from the frame bundle of the target manifold $N$. Given a parallelized $m$-manifold $M$ and an $n$-manifold $N$ equipped with a…
In a previous work, by extending the classical Quillen construction to the non-simply connected case, we have built a pair of adjoint functors, 'model' and 'realization', between the categories of simplicial sets and complete differential…
This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a…
This article is an introduction to the basic generalized category theory used in recent work on an extension of the theory of categories and categorical logic, including parts of topos theory. We discuss functors, equivalences, natural…
We construct invariants of four-dimensional piecewise-linear manifolds, represented as simplicial complexes, with respect to rebuildings that transform a cluster of three 4-simplices having a common two-dimensional face in a different…
A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as…
In this paper, we present a unified approach using model category theory and an associative law to compare some classic variants of the geometric realization functor.
We study the splitting of the Goodwillie towers of functors in various settings. In particular, we produce splitting criteria for functors $F: \A \to M_A$ from a pointed category with coproducts to $A$-modules in terms of differentials of…
We associate to a bimonoidal functor, i.e. a bifunctor which is monoidal in each variable, a nonabelian version of a biextension. We show that such a biextension satisfies additional triviality conditions which make it a bilinear analog of…
We redefine the Baum-Connes assembly map using simplicial approximation in the equivariant Kasparov category. This new interpretation is ideal for studying functorial properties and gives analogues of the assembly maps for all equivariant…
We define the notion of an approximate triangulation for a manifold $M$ embedded in euclidean space. The basic idea is to build a nested family of simplicial complexes whose vertices lie in $M$ and use persistent homology to find a complex…
On a symplectic manifold, there is a natural elliptic complex replacing the de Rham complex. It can be coupled to a vector bundle with connection and, when the curvature of this connection is constrained to be a multiple of the symplectic…
We construct a functor from the category of graphs to the category of groups which is faithful and "almost" full, in the sense that it induces bijections of the Hom sets up to trivial homomorphisms and conjugation in the category of groups.…
We introduce a category of extended complex manifolds, and prove that the functor describing deformations of a classical compact complex manifold $M$ within this category is versally representable by (an analytic subspace in) $H^*(M,T_M)$.…
In this paper we generalize to a certain class of Stein manifolds the Bernstein-Walsh-Siciak theorem which describes the equivalence between possible holomorphic continuation of a function $f$ defined on a compact set $K$ in $\mathbb{C}^N$…
We discuss generalised duality theory for monoidal categories and its applications to the categories of exact endofunctors, graded vector spaces, and topological vector spaces.
I explain a direct approach to differentiation and integration. Instead of relying on the general notions of real numbers, limits and continuity, we treat functions as the primary objects of our theory, and view differentiation as division…
In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. We give several simple examples of Riemannian…
In this paper we classify endofunctors on the simplex category, and we identify those that induce weak equivalence preserving functors on the category of simplicial sets.