Related papers: A model for framed configuration spaces of points
We construct proper good moduli spaces for moduli stacks of Bridgeland semistable orthosymplectic complexes on a complex smooth projective variety, which we propose as a candidate for compactifying moduli spaces of principal bundles for the…
We show that one can characterize the Besov spaces on a smooth compact oriented Riemannian manifold, for the full range of indices, through a knowledge of the size of frame coefficients, using the frames we have constructed in [8].
We present several naturally occurring classes of spectral spaces using commutative algebra on pointed monoids. For this purpose, our main tools are finite type closure operations and continuous valuations on monoids which we introduce in…
In this article we show that every closed orientable smooth $4$--manifold admits a smooth embedding in the complex projective $3$--space.
The homology of configuration spaces of point-particles in manifolds has been studied intensively since the 1970s; in particular it is known to be stable if the underlying manifold is connected and open. Closely related to configuration…
The moduli space of regular stable maps with values in a complex manifold admits naturally the structure of a complex orbifold. Our proof uses the methods of differential geometry rather than algebraic geometry. It is based on Hardy…
This paper investigates mapping spaces between enriched operads and relates these spaces to those between operadic bimodules via convenient fiber sequences. The main statements hold for simplicial operads, operads enriched in simplicial…
It is shown that every algebra over the chain operad of the little disks operad gives naturally rise to a Hertling-Manin's F-manifold, that is a smooth manifold equipped with an integrable graded commutative associative product on the…
Operads are algebraic devices offering a formalization of the concept of operations with several inputs and one output. Such operations can be naturally composed to form bigger and more complex ones. Coming historically from algebraic…
From Smyth's classification, modular compactifications of pointed smooth rational curves are indexed by combinatorial data, so-called extremal assignments. We explore their combinatorial structures and show that any extremal assignment is a…
An oriented compact closed manifold is called inflexible if the set of mapping degrees ranging over all continuous self-maps is finite. Inflexible manifolds have become of importance in the theory of functorial semi-norms on homology.…
Folding is emerging as a promising manufacturing process to transform flat materials into functional structures, offering efficiency by reducing the need for welding, gluing, and molding, while minimizing waste and enabling automation.…
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of geometric properties of smooth manifolds. Round fold maps were introduced as stable fold maps…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…
We study polygon spaces arising from planar configurations of necklaces with some of the beads fixed and some of the beads sliding freely. These spaces include configuration spaces of flexible polygons and some other natural polygon spaces.…
The functor that takes a manifold to its configuration category exhibits a type of full faithfulness in some cases.
We consider the space of embeddings of finitely many circles that bound disks in non-positively curved surfaces. We index the connected components of this space with finite rooted trees and show that the connected components are classifying…
Using the language of twisted skew-commutative algebras, we define \emph{secondary representation stability}, a stability pattern in the {\it unstable} homology of spaces that are representation stable in the sense of Church, Ellenberg, and…
Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…
This paper is a survey of the relationship between labelled configuration spaces, mapping class groups with marked points and function spaces. In particular, we collect calculations of the cohomology groups for the mapping class groups of…