Related papers: Algebraic models of Poincare embeddings

Let $W$ be a finite Weyl group of classical type which may not be irreducible, $F$ an algebraically closed field, $q$ an invertible element of $F$. We denote by $\mathcal H_W(q)$ the associated Hecke algebra. If $q=1$ then it is $FW$ and we…

We show Poincar\'e Duality for $\mathbf{F}_p$-\'etale cohomology of a smooth proper rigid-analytic space over a non-archimedean field $K$ of mixed characteristic $(0, p)$. It positively answers the question raised by P. Scholze in [Sch13a].…

Let M be a simply-connected closed Poincare Duality complex of dimension n. Then M is obtained by attaching a cell of highest dimension to its (n-1)-skeleton M'. Conditions are given for when the skeletal inclusion i:M' --> M has the…

The polytope subalgebra of deformations of a zonotope can be endowed with the structure of a module over the Tits algebra of the corresponding hyperplane arrangement. We explore this construction and find relations between statistics on…

The homotopy type of the complement of a complex coordinate subspace arrangement is studied by fathoming out the connection between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy…

We establish a loop space decomposition for certain $CW$-complexes with a single top cell in the presence of a spherical pair, thereby generalizing several known decompositions of Poincar\'{e} duality complexes in which a loop of a product…

It is shown that optical geometry of the Reissner-Nordstrom exterior metric can be embedded in a hyperbolic space all the way down to its outer horizon. The adopted embedding procedure removes a breakdown of flat-space embeddings which…

Let X be a compact connected Riemann surface. Fix a positive integer r and two nonnegative integers d_p and d_z. Consider all pairs of the form (F, f), where F is a holomorphic vector bundle on X of rank r and degree d_z-d_p, and f :…

We exhibit a Poisson module restoring a twisted Poincare duality between Poisson homology and cohomology for the polynomial algebra R=C[X_1,...,X_n] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This…

A polynomial knot in $\mathbb{R}^n$ is a smooth embedding of $\mathbb{R}$ in $\mathbb{R}^n$ such that the component functions are real polynomials. In the earlier paper with Mishra, we have studied the space $\mathcal{P}$ of polynomial…

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We…

In this paper we use the technique of Hopf algebras and quasi-symmetric functions to study the combinatorial polytopes. Consider the free abelian group $\mathcal{P}$ generated by all combinatorial polytopes. There are two natural bilinear…

We describe a fully faithful embedding of the category of (reflexive) globular sets into the category of counital cosymmetric $R$-coalgebras when $R$ is an integral domain. This embedding is a lift of the usual functor of $R$-chains and the…

Any planar shape $P\subset \mathbb{C}$ can be embedded isometrically as part of the boundary surface $S$ of a convex subset of $\mathbb{R}^3$ such that $\partial P$ supports the positive curvature of $S$. The complement $Q = S \setminus P$…

We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability…

Given a symmetric operad $\mathcal{P}$ and a $\mathcal{P}$-algebra $V$, the associative universal enveloping algebra ${\mathsf{U}_{\mathcal{P}}}$ is an associative algebra whose category of modules is isomorphic to the abelian category of…

A wealth of geometric and combinatorial properties of a given linear endomorphism $X$ of $\R^N$ is captured in the study of its associated zonotope $Z(X)$, and, by duality, its associated hyperplane arrangement ${\cal H}(X)$. This…

The Wythoff construction takes a $d$-dimensional polytope $P$, a subset $S$ of $\{0,..., d\}$ and returns another $d$-dimensional polytope $P(S)$. If $P$ is a regular polytope, then $P(S)$ is vertex-transitive. This construction builds a…

Two cochain complexes are constructed for an algebra A and a coalgebra C entwined with each other via the map $\psi:C\otimes A\to A\otimes C$. One complex is associated to an A-bimodule, the other to a C-bicomodule. In the former case the…

Let V be a cofibrantly generated closed symmetric monoidal model category and M a model V-category. We say that a weighted colimit W*D of a diagram D weighted by W is a homotopy weighted colimit if the diagram D is pointwise cofibrant and…