Study smooth manifolds using disc-presheaves.
problem Understanding smooth manifolds.
method Using presheaves on a category of discs.
result Disc-presheaves have desirable properties and strong applications.
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14 results for “presheaves”
Researchers compute differential K-theory for moduli stacks.
problem Computing differential K-theory for moduli stacks of principal G-bundles.
method Using homotopy theory of presheaves of spaces and spectra, they formulate results in terms of invariant polynomials and representation rings.
result They successfully compute the connective differential K-theory and differential cohomology of moduli stacks.
Detecting exotic spheres involves analyzing framed configuration spaces.
problem Detecting exotic spheres through homotopy type of truncated Disc-presheaves.
method Using gluing results for Disc-presheaves, Atiyah duality, and computations of mapping class groups.
result Conditions for detecting exotic spheres through framed configuration spaces.
Study homotopy sheaves on categories and their presheaves, proving descent properties.
problem Homotopy sheaves on categories and their presheaves.
method Homotopy right Kan extension, pretopologies, Yoneda embedding.
result Preserves homotopy sheaves and induces equivalence between sheaves and colimit-preserving sheaves.
We describe the moduli space of extensions in the model category of simplicial presheaves. This article can be seen as a generalization of Blomgren-Chacholski results in the case of simplicial sets. Our description of the moduli space of extensions treat the equivariant and the nonequivariant case in the same setting. …
The paper bridges diffeological bundle theory with higher topos theory.
problem Comparing Čech cohomology of diffeological spaces with existing notions.
method Using Čech model structure on simplicial presheaves and diffeological spaces as discrete simplicial presheaves.
result Nerve of diffeological principal -bundles is weak homotopy equivalent to -principal -bundles.
In this paper we introduce -manifolds as generalizations of the notion of smooth manifolds with -structure or with -bounded geometry. These are -manifolds whose transition functions are such that $\partial^μ\varphi_{ji}\in B_{α(r)}\cap C^{k-β(r)}…
New method constructs tilings of the plane using directed edges and alignments.
problem Modeling tilings of the Euclidean or hyperbolic plane as presheaves over categories.
method Introducing finite categories for polygons with labeled directed edges, constructing reflective alignments.
result Characterizing alignments of tilings by comparing edge directions and generating families with elegant symmetry.
In this article we give an equivariant version for the construction of generic models on presheaves of structures. We deal with first order structures endowed with a suitable action of some fixed group, say ; we call them -structures. We show that every exact presheaf of -structures has a generic…
Abstract: Generalizes Milnor-Schwarz lemma to inverse monoids.
problem Applying Milnor-Schwarz lemma to inverse monoids.
method Two proofs provided: elementary and using Vietoris-Rips complex.
result Generalization of Milnor-Schwarz lemma to inverse monoids.
Projective model structures on diffeological spaces and smooth sets and the smooth Oka principlemath.AT
Smooth structures on diffeological spaces and sheaves, resolving conjectures.
problem Model structures on diffeological spaces and sheaves of sets.
method Embedding diffeological spaces into sheaves of sets, studying combinatorial model structures, and proving equivalence to simplicial sets.
result Established a model structure on sheaves of sets that is Quillen equivalent to simplicial sets and has properties like cartesian and cofibrant smooth manifolds.
Study of embedding spaces using homotopy theory and operads.
problem Understanding the stable homotopy type of embedding spaces.
method Analysis of cubes of framed configuration spaces, homotopy theory of presheaves, operadic structures.
result Induced action of the Poisson operad on the homology of configuration spaces is a homotopy invariant.
Localizes smooth spaces to study their homotopy properties.
problem Understanding the homotopy theory of smooth spaces.
method Model category localization, Quillen equivalences, fibrant replacement.
result Localisation of smooth spaces agrees with motivic-style -localisation.
Khovanov homology for pro-tangles and spectral sequences
problem Developing a framework for Khovanov homology for pro-tangles and spectral sequences
method Using pro-tangles, simplicial presheaves, and spectral sequences
result Establishing a fully faithful embedding and an algebraic spectral sequence for pro-tangles