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We study the blow-down map in cohomology in the context of real projective blowups of Lie algebroids. Using the blow-down map in cohomology we compute the Lie algebroid cohomology of the blowup of transversals of arbitrary codimension,…
In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse…
We present a Geometric Invariant Theory (GIT) construction which allows us to construct good projective degenerations of Hilbert schemes of points for simple degenerations. A comparison with the construction of Li and Wu shows that our GIT…
We show that the topology of uniform convergence on bounded sets is compatible with the group law of the automorphism group of a large class of spaces that are endowed with both a uniform structure and a bornology, thus yielding numerous…
We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typical way to stabilize manifolds. In particular, we show a loop homotopy decomposition of a manifold after stabilization by a projective space,…
In these lectures, we provide a toolkit to work with Chow-Witt groups, and more generally with the homology and cohomology of the Rost-Schmid complex associated to Milnor-Witt $K$-theory.
In this paper, an algorithm building the effective homology version of the pushout of the simplicial morphisms $f:X\rightarrow Y$ and $g:X\rightarrow Z$, where $X,Y$ and $Z$ are simplicial sets with effective homology is presented.
There are several different proposals, relating holographic complexity to the gravitational objects defined on the Wheeler-DeWitt patch. In this paper, we investigate the evolution of complexity following a global quantum quench for these…
In this paper, we are interested in the location of conjugate points along a geodesic in the volumorphism group of a compact three-dimensional manifold without boundary (the configuration space of an ideal fluid). As shown in the author's…
The local classification of conformally flat Lorentzian manifolds with special holonomy groups is obtained. The corresponding local metrics are certain extensions of Riemannian spaces of constant sectional curvature to Walker metrics.
We study the Hochschild homology of the convolution algebra of a proper Lie groupoid by introducing a convolution sheaf over the space of orbits. We develop a localization result for the associated Hochschild homology sheaf, and prove that…
We develop a Hamiltonian description of point particles in (2+1)-dimensions using connection and frame-field variables for general relativity. The topology of each spatial hypersurface is that of a punctured two-sphere with particles…
The exact or Wilson renormalization group equations can be formulated as a functional Fokker-Planck equation in the infinite-dimensional configuration space of a field theory, suggesting a stochastic process in the space of couplings.…
We show that for topological groups and loop contractible coefficients the cohomology groups of continuous group cochains and of group cochains that are continuous on some identity neighbourhood are isomorphic. Moreover, we show a similar…
We give a general description of the structure of the relative de Rham-Witt complex on a polynomial ring, seen as an algebra over its integral part. After giving a control of the overconvergence of Lazard's morphism, we similarly give the…
We introduce homological and homotopical $r$-syzygies of Mori fibre spaces as a generalization of Sarkisov links and relations of Sarkisov links. For any proper morphism $Y/R$, we construct a contractible (if not empty) CW complex such that…
We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…
The paper has two parts, in the first part, we apply the localisation technique to the Rozansky-Witten theory on compact HyperK\"ahler targets. We do so via first reformulating the theory as some supersymmetric sigma-model. We obtain the…
We provide a representation of the homomorphisms $U\longrightarrow \mathbb R$, where $U$ is the lattice of all uniformly continuous on the line. The resulting picture is sharp enough to describe the fine topological structure of the space…
Using deformations of foliations to contact structures as well as rigidity properties of Anosov foliations we provide infinite families of examples which show that the space of taut foliations in a given homotopy class of plane fields is in…