Related papers: Homomorphisms of infinitely generated analytic she…

We show that, on a closed semipositive symplectic manifold with semisimple quantum homology, any Hamiltonian diffeomorphism possessing more contractible fixed points, counted homologically, than the total Betti number of the manifold, must…

Given a compact hyperkaehler manifold $M$ and a holomorphic bundle B over $M$, we consider a Hermitian connection $\nabla$ on B which is compatible with all complex structures on $M$ induced by the hyperkaehler structure. Such a connection…

A holomorphic germ \Phi: (C^2, 0) \to (C^3, 0), singular only at the origin, induces at the links level an immersion of S^3 into S^5. The regular homotopy type of such immersions are determined by their Smale invariant, defined up to a sign…

We prove that random $\mathbb{Z}$-homomorphisms on weakly expanding bipartite graphs exhibit a strong "flatness" phenomenon. Extending prior work of Peled, Samotij, and Yehudayoff for expanders, we first show that on any bipartite $(n, d,…

Given a closed smooth manifold $M$ of even dimension $2n\ge6$ with finite fundamental group, we show that the classifying space ${\rm BDiff}(M)$ of the diffeomorphism group of $M$ is of finite type and has finitely generated homotopy groups…

We show how to attach to any rigid analytic variety $V$ over a perfectoid space $P$ a rigid analytic motive over the Fargues-Fontaine curve $\mathcal{X}(P)$ functorially in $V$ and $P$. We combine this construction with the overconvergent…

It is known by a result of Mendes and Sampaio that the Lipschitz normal embedding of a subanalytic germ is fully characterized by the Lipschitz normal embedding of its link. In this note, we show that the result still holds for definable…

Let $(M,Q)$ be a compact, three dimensional manifold of strictly negative sectional curvature. Let $(\Sigma,P)$ be a compact, orientable surface of hyperbolic type (i.e. of genus at least two). Let $\theta:\pi_1(\Sigma,P)\to\pi_1(M,Q)$ be a…

We identify the holomorphic de Rham complex of the minimal extension of a meromorphic vector bundle with connexion on a compact Riemann surface X with the L^2 complex relative to a suitable metric on the bundle and a complete metric on the…

Starting point of the present work is a conjecture of F. Catanese which says that in the derived category of coherent sheaves on any rational homogeneous manifold G/P there should exist a complete strong exceptional poset and a bijection of…

If P \to X is a topological principal K-bundle and \hat K a central extension of K by Z, then there is a natural obstruction class \delta_1(P) in \check H^2(X,\uline Z) in sheaf cohomology whose vanishing is equivalent to the existence of a…

In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett theorem can be combined with a sufficiently well behaved homomorphisms. In this paper we will show that those combined extensions can be made if we…

We prove that the linearization of a germ of holomorphic map of the type $F_\lambda(z)=\lambda(z+O(z^2))$ has a $ C^1$--holomorphic dependence on the multiplier $\lambda$. $C^1$--holomorphic functions are $ C^1$--Whitney smooth functions,…

It is well known [Lov\'asz, 67] that up to isomorphism a graph~$G$ is determined by the homomorphism counts $\hom(F, G)$, i.e., the number of homomorphisms from $F$ to $G$, where $F$ ranges over all graphs. Thus, in principle, we can answer…

Let $\widehat{\mathcal{G}}^{(\lambda)}$ be a formal group scheme which deforms $\widehat{\mathbb{G}}_a$ to $\widehat{\mathbb{G}}_m$. And let $\psi^{(l)}:\widehat{\mathcal{G}}^{(\lambda)}\rightarrow\widehat{\mathcal{G}}^{(\lambda^{p^l})}$ be…

The Hales-Jewett Theorem states that given any finite nonempty set $\A$ and any finite coloring of the free semigroup $S$ over the alphabet $\A$ there is a {\it variable word\/} over $\A$ all of whose instances are the same color. This…

We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module…

We show that conically smooth stratified spaces embed fully faithfully into $\infty$-categories. This articulates a stratified generalization of the homotopy hypothesis proposed by Grothendieck. As such, each $\infty$-category defines a…

For a local non-Archimedean field $K$ we construct ${\rm GL}_{d+1}(K)$-equivariant coherent sheaves ${\mathcal V}_{{\mathcal O}_K}$ on the formal ${\mathcal O}_K$-scheme ${\mathfrak X}$ underlying the symmetric space $X$ over $K$ of…

A classical result due to Lovasz (1967) shows that the isomorphism type of a graph is determined by homomorphism counts. That is, graphs G and H are isomorphic whenever the number of homomorphisms from K to G is the same as the number of…