A proof of Reidemeister-Singer’s theorem by Cerf’s methods

François Laudenbach

Displaying similar documents to “A proof of Reidemeister-Singer’s theorem by Cerf’s methods”

Multi-Harnack smoothings of real plane branches

Pedro Daniel González Pérez, Jean-Jacques Risler (2010)

Annales scientifiques de l'École Normale Supérieure

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Let $Δ \subset 𝐑^{2}$ be an integral convex polygon. G. Mikhalkin introduced the notion of, a class of real algebraic curves, defined by polynomials supported on $Δ$ and contained in the corresponding toric surface. He proved their existence, viamethod, and that the topological type of their real parts is unique (and determined by $Δ$ ). This paper is concerned with the description of the analogous statement in the case of a smoothing of a real plane branch $(C, 0)$ . We introduce the class ofsmoothings of $(C, 0)$ by...

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

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Let (Ω, $ℱ$ , ( $ℱ_{t}$ ), $ℙ$ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to $ℱ_{\infty}$ (the-algebra generated by ( $ℱ_{t}$ )) a coherent family of probability measures ( $ℚ_{t}$ ) indexed by , each of them being defined on $ℱ_{t}$ . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative...

A priori bounds for some infinitely renormalizable quadratics: II. Decorations

Jeremy Kahn, Mikhail Lyubich (2008)

Annales scientifiques de l'École Normale Supérieure

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A decoration of the Mandelbrot set $M$ is a part of $M$ cut off by two external rays landing at some tip of a satellite copy of $M$ attached to the main cardioid. In this paper we consider infinitely renormalizable quadratic polynomials satisfying the decoration condition, which means that the combinatorics of the renormalization operators involved is selected from a finite family of decorations. For this class of maps we prove bounds. They imply local connectivity of the corresponding Julia...

Constructive quantization: approximation by empirical measures

Steffen Dereich, Michael Scheutzow, Reik Schottstedt (2013)

Annales de l'I.H.P. Probabilités et statistiques

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In this article, we study the approximation of a probability measure $μ$ on $ℝ^{d}$ by its empirical measure ${\hat{μ}}_{N}$ interpreted as a random quantization. As error criterion we consider an averaged $p$ th moment Wasserstein metric. In the case where $2 p l t; d$ , we establish fine upper and lower bounds for the error, a. Moreover, we provide a universal estimate based on moments, a . In particular, we show that quantization by empirical measures is of optimal order under weak assumptions.

Curvature measures, normal cycles and asymptotic cones

Xiang Sun, Jean-Marie Morvan (2013)

Actes des rencontres du CIRM

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The purpose of this article is to give an overview of the theory of the and to show how to use it to define a on singular surfaces embedded in an (oriented) Euclidean space $𝔼^{3}$ . In particular, we will introduce the notion of associated to a Borel subset of $𝔼^{3}$ , generalizing the defined at each point of a smooth surface. For simplicity, we restrict our singular subsets to polyhedra of the $3$ -dimensional Euclidean space $𝔼^{3}$ . The coherence of the theory lies in a convergence theorem: If a...

Waring’s problem for Beatty sequences and a local to global principle

William D. Banks, Ahmet M. Güloğlu, Robert C. Vaughan (2014)

Journal de Théorie des Nombres de Bordeaux

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We investigate in various ways the representation of a large natural number $N$ as a sum of $s$ positive $k$ -th powers of numbers from a fixed Beatty sequence. , a very general form of the local to global principle is established in additive number theory. Although the proof is very short, it depends on a deep theorem of M. Kneser.

The jacobian map, the jacobian group and the group of automorphisms of the Grassmann algebra

Vladimir V. Bavula (2010)

Bulletin de la Société Mathématique de France

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There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras (e.g., the Grassmann algebras are dual of polynomial algebras as quadratic algebras). This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set– the set of all algebra endomorphisms of a polynomial algebra with the Jacobian...

Some results on spaces with $ℵ_{1}$ -calibre

Wei-Feng Xuan, Wei-Xue Shi (2016)

Commentationes Mathematicae Universitatis Carolinae

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We prove that, assuming , if $X$ is a space with $ℵ_{1}$ -calibre and a zeroset diagonal, then $X$ is submetrizable. This gives a consistent positive answer to the question of Buzyakova in Observations on spaces with zeroset or regular $G_{δ}$ -diagonals, Comment. Math. Univ. Carolin. 46 (2005), no. 3, 469–473. We also make some observations on spaces with $ℵ_{1}$ -calibre.

Ricci flow coupled with harmonic map flow

Reto Müller (2012)

Annales scientifiques de l'École Normale Supérieure

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We investigate a coupled system of the Ricci flow on a closed manifold $M$ with the harmonic map flow of a map $φ$ from $M$ to some closed target manifold $N$ , $\frac{\partial}{\partial t} g = - 2 Rc + 2 α \nabla φ \otimes \nabla φ, \frac{\partial}{\partial t} φ = τ_{g} φ,$ where $α$ is a (possibly time-dependent) positive coupling constant. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of $φ$ a-priori by choosing $α$ large enough. Moreover, it suffices to bound the curvature...

Cutting the loss of derivatives for solvability under condition $(Ψ)$

Nicolas Lerner (2006)

Bulletin de la Société Mathématique de France

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For a principal type pseudodifferential operator, we prove that condition $(ψ)$ implies local solvability with a loss of 3/2 derivatives. We use many elements of Dencker’s paper on the proof of the Nirenberg-Treves conjecture and we provide some improvements of the key energy estimates which allows us to cut the loss of derivatives from $ϵ + 3 / 2$ for any $ϵ > 0$ (Dencker’s most recent result) to 3/2 (the present paper). It is already known that condition $(ψ)$ doesimply local solvability with a loss of 1...

On standard norm varieties

Nikita A. Karpenko, Alexander S. Merkurjev (2013)

Annales scientifiques de l'École Normale Supérieure

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Let $p$ be a prime integer and $F$ a field of characteristic $0$ . Let $X$ be theof a symbol in the Galois cohomology group $H^{n + 1} (F, μ_{p}^{\otimes n})$ (for some $n \geq 1$ ), constructed in the proof of the Bloch-Kato conjecture. The main result of the paper affirms that the function field $F (X)$ has the following property: for any equidimensional variety $Y$ , the change of field homomorphism $CH (Y) \to CH (Y_{F (X)})$ of Chow groups with coefficients in integers localized at $p$ is surjective in codimensions $< (dim X) / (p - 1)$ . One of the main ingredients of the proof is a computation...

Piecewise linear approximation of smooth functions of two variables

Joseph H.G. Fu (2013)

Actes des rencontres du CIRM

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The normal cycle of a singular subset $X$ of a smooth manifold is a basic tool for understanding and computing the curvature of $X$ . If $X$ is replaced by a singular function on $ℝ^{n}$ then there is a natural companion notion called the of $f$ , which has been introduced by the author and by R. Jerrard. We discuss a few fundamental facts and open problems about functions $f$ that admit gradient cycles, with particular attention to the first nontrivial dimension $n = 2$ .

The parabolic Anderson model in a dynamic random environment: Basic properties of the quenched Lyapunov exponent

D. Erhard, F. den Hollander, G. Maillard (2014)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper we study the parabolic Anderson equation $\partial u (x, t) / \partial t = κ 𝛥 u (x, t) + ξ (x, t) u (x, t)$ , $x \in ℤ^{d}$ , $t \geq 0$ , where the $u$ -field and the $ξ$ -field are $ℝ$ -valued, $κ \in [0, \infty)$ is the diffusion constant, and $𝛥$ is the discrete Laplacian. The $ξ$ -field plays the role of athat drives the equation. The initial condition $u (x, 0) = u_{0} (x)$ , $x \in ℤ^{d}$ , is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate $2 d κ$ ,...

Dimers and cluster integrable systems

Alexander B. Goncharov, Richard Kenyon (2013)

Annales scientifiques de l'École Normale Supérieure

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We show that the dimer model on a bipartite graph $Γ$ on a torus gives rise to a quantum integrable system of special type, which we call a. The phase space of the classical system contains, as an open dense subset, the moduli space $Ł_{Γ}$ of line bundles with connections on the graph $Γ$ . The sum of Hamiltonians is essentially the partition function of the dimer model. We say that two such graphs $Γ_{1}$ and $Γ_{2}$ areif the Newton polygons of the corresponding partition functions coincide up to translation....

Limit theorems for one and two-dimensional random walks in random scenery

Fabienne Castell, Nadine Guillotin-Plantard, Françoise Pène (2013)

Annales de l'I.H.P. Probabilités et statistiques

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Random walks in random scenery are processes defined by $Z_{n} : = \sum_{k = 1}^{n} ξ_{X_{1} + \dots + X_{k}}$ , where $(X_{k}, k \geq 1)$ and $(ξ_{y}, y \in ℤ^{d})$ are two independent sequences of i.i.d. random variables with values in $ℤ^{d}$ and $ℝ$ respectively. We suppose that the distributions of $X_{1}$ and $ξ_{0}$ belong to the normal basin of attraction of stable distribution of index $α \in (0, 2]$ and $β \in (0, 2]$ . When $d = 1$ and $α \neq 1$ , a functional limit theorem has been established in ( (1979) 5–25) and a local limit theorem in (To appear). In this paper, we establish the convergence in distribution...