Related papers: Thom condition and Monodromy

In this very short paper, we provide a strong motivation for the study of the following problem: given a real normed space $E$, a closed, convex, unbounded set $X\subseteq E$ and a function $f:X\to X$, find suitable conditions under which,…

A simplicial complex $X$ is said to be tight with respect to a field $\mathbb{F}$ if $X$ is connected and, for every induced subcomplex $Y$ of $X$, the linear map $H_\ast (Y; \mathbb{F}) \rightarrow H_\ast (X; \mathbb{F})$ (induced by the…

Let $S$ be a compact Hausdorff space and $X$ a complex manifold. We consider the space $C(S,X)$ of continuous maps $S\to X$, and prove that any bounded holomorphic function on this space can be continued to a holomorphic function, possibly…

We present a new sufficient condition under which a maximal monotone operator $T:X\tos X^*$ admits a unique maximal monotone extension to the bidual $\widetilde T:X^{**} \rightrightarrows X^*$. For non-linear operators this condition is…

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.

We prove that any finite subgroup $G \subset \Gamma_{{\boldsymbol{s}}}$ of the cluster modular group has fixed points in the cluster manifolds $\mathcal{A}_{\boldsymbol{s}}(\mathbb{R}_{>0})$ and…

We prove an "abelian, locally compact" Whitehead theorem in fine shape: A fine shape morphism between locally connected finite-dimensional locally compact separable metrizable spaces with trivial $\pi_0$ and $\pi_1$ is a fine shape…

Let $X$ be a general complex projective hypersurface in $\mathbb{P}^{n+1}$ of degree $d>1$. A point $P$ not in $X$ is called uniform if the monodromy group of the projection of $X$ from $P$ is isomorphic to the symmetric group. We prove…

We prove that if a continuous piecewise-smooth map on $\mathbb{R}^n$ is comprised of two linear functions, has a bounded orbit, and satisfies a certain non-degeneracy condition, then it has a fixed point. The result has important…

We extend the proof of Reifenberg's Topological Disk Theorem to allow the case of sets with holes, and give sufficient conditions on a set $E$ for the existence of a bi-Lipschitz parameterization of $E$ by a $d$-dimensional plane or smooth…

We establish certain conditions which imply that a map $f:X\to Y$ of topological spaces is null homotopic when the induced integral cohomology homomorphism is trivial; one of them is: $H^*(X)$ and $\pi_*(Y)$ have no torsion and $H^*(Y)$ is…

We prove the following two results 1. For a proper holomorphic function $ f : X \to D$ of a complex manifold $X$ on a disc such that $\{df = 0 \} \subset f^{-1}(0)$, we construct, in a functorial way, for each integer $p$, a geometric…

An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…

In the present work we obtain rigidity results analysing the set of regular points, in the sense of Oseledec's Theorem. It is presented a study on the possibility of an Anosov diffeomorphisms having all Lyapunov exponents defined…

Thom polynomial describes the cohomology class Poincar\'e dual to the locus of particular singularity of a generic holomorphic map. In this paper we derive a closed formula for the generating function of its coefficients. The method is…

Let $\mathfrak g$ be a simple complex Lie algebra of finite dimension. This paper gives an inequality relating the order of an automorphism of $\mathfrak g$ to the dimension of its fixed-point subalgebra, and characterizes those…

Transformation monoids carry a canonical topology --- the topology of point-wise convergence. A closed transformation monoid $\mathfrak{M}$ is said to have automatic homeomorphicity with respect to a class $\mathcal{K}$ of structures, if…

Let $X$ and $Y$ be compact K\"ahler manifolds of dimension $3$. A bimeromorphic map $f:X\rightarrow Y$ is pseudo-isomorphic if $f:X-I(f)\rightarrow Y-I(f^{-1})$ is an isomorphism. Let $T=T^+-T^-$ be a current on $Y$, where $T^{\pm}$ are…

For a given category C and a topological space X, the constant stack on X with stalk C is the stack of locally constant sheaves with values in C. Its global objects are classified by their monodromy, a functor from the Poincare groupoid of…

If $(M,g)$ is a compact real analytic Riemannian manifold, we give a necessary and sufficient condition for there to be a sequence of quasimodes of order $o(\lambda)$ saturating sup-norm estimates. In particular, it gives optimal conditions…