Related papers: Local rigid cohomology of singular points

We show an intrinsic version of Thomason's fixed-point theorem. Then we determine the local structure of the Hilbert scheme of at most $7$ points in $\mathbb{A}^3$. In particular, we show that in these cases, the points with the same extra…

We study the classification of closed, smooth, spin, $1$-connected $7$-manifolds whose integral cohomology ring is isomorphic to $H^*(\mathbb{C}P^2\times S^3)$. We also prove that if the integral cohomology ring of a closed, smooth, spin,…

In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR compactum and x\in X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of…

In this paper, we connect the rigidity problem and the coarse Baum-Connes conjecture for Roe algebras. In particular, we show that if $X$ and $Y$ are two uniformly locally finite metric spaces such that their Roe algebras are…

Let $X(P,\lambda)$ be a 4-dimensional toric orbifold associated to a polygon $P$ and a characteristic function $\lambda$. Assuming that $X(P,\lambda)$ is locally smooth over a vertex of $P$, we determine the integral cohomology ring…

In this paper we study the structure of cohomology spaces for the Frobenius kernels of unipotent and parabolic algebraic group schemes and of their quantum analogs. Given a simple algebraic group $G$, a parabolic subgroup $P_J$, and its…

We compute the cohomology ring of a generalised type of configuration space of points in $\mathbb{R}^r$. This configuration space is indexed by a graph. In the case the graph is complete the result is known and it is due to Arnold and…

We prove that, if two germs of plane curves $(C,0)$ and $(C',0)$ with at least one singular branch are equivalent by a (real) smooth diffeomorphism, then $C$ is complex isomorphic to $C'$ or to $\overline{C'}$. A similar result was shown by…

In this article we prove that locally Griffiths' horizontal distribution on the period domain is given by a generalized version of the familiar contact differential system. As a consequence of this description we obtain strong local…

The space $\Gamma_X$ of all locally finite configurations in a Riemannian manifold $X$ of infinite volume is considered. The deRham complex of square-integrable differential forms over $\Gamma_X$, equipped with the Poisson measure, and the…

We formulate the notion of an isomorphism of GKM graphs. We then show that two GKM graphs have isomorphic graph equivariant cohomology algebras if and only if the graphs are isomorphic.

We determine the algebra structure of the Hochschild cohomology of the singular cochain algebra with coefficients in a field on a space whose cohomology is a polynomial algebra. A spectral sequence calculation of the Hochschild cohomology…

Given a graded complete intersection ideal $J = (f_1, \dots, f_c) \subseteq k[x_0, \dots, x_n] = S$, where $k$ is a field of characteristic $p > 0$ such that $[k:k^p] < \infty$, we show that if $S/J$ has an isolated non-F-pure point then…

Chen and Ruan's orbifold cohomology of the symmetric product of a complex manifold is calculated. An isomorphism of rings (up to a change of signs) $H_{orb}^*(X^n/S_n;\complex) \cong H^*(X^{[n]};\complex)$ between the orbifold cohomology of…

Given a Fell bundle $\mathscr C\overset{q}{\to}\Xi$ over the discrete groupoid $\Xi$, we study the symmetry of the associated Hahn algebra $\ell^{\infty,1}(\Xi\!\mid\!\mathscr C)$ in terms of the isotropy subgroups of $\Xi$. We prove that…

We prove that the deformation space $AH(M)$ of marked hyperbolic 3-manifolds homotopy equivalent to a fixed compact 3-manifold $M$ with incompressible boundary is locally connected at quasiconformally rigid points.

In this paper a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg…

We introduce smooth L^\infty differential forms on a singular (semialgebraic) set X in R^n. Roughly speaking, a smooth L^\infty differential form is a certain class of equivalence of 'stratified forms', that is, a collection of smooth forms…

We investigate the local deformation space of 3-dimensional cone-manifold structures of constant curvature $\kappa \in \{-1,0,1\}$ and cone-angles $\leq \pi$. Under this assumption on the cone-angles the singular locus will be a trivalent…

Let $(X,g)$ be a compact Riemannian stratified space with simple edge singularity. Thus a neighbourhood of the singular stratum is a bundle of truncated cones over a lower dimensional compact smooth manifold. We calculate the various…