A continuous Helson surface in ${\bf R}^3$

Detlef Müller

Displaying similar documents to “A continuous Helson surface in $𝐑^{3}$ ”

A proof of the crossing number of $K_{3, n}$ in a surface

Pak Tung Ho (2007)

Discussiones Mathematicae Graph Theory

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In this note we give a simple proof of a result of Richter and Siran by basic counting method, which says that the crossing number of $K_{3, n}$ in a surface with Euler genus ε is ⎣n/(2ε+2)⎦ n - (ε+1)(1+⎣n/(2ε+2)⎦).

Construction techniques for some thin sets in duals of compact abelian groups

D. J. Hajela (1986)

Annales de l'institut Fourier

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Various techniques are presented for constructing $Λ$ (p) sets which are not $Λ (p + ϵ)$ for all $ϵ > 0$ . The main result is that there is a $Λ$ (4) set in the dual of any compact abelian group which is not $Λ (4 + ϵ)$ for all $ϵ > 0$ . Along the way to proving this, new constructions are given in dual groups in which constructions were already known of $Λ$ (p) not $Λ (p + ϵ)$ sets, for certain values of $p$ . The main new constructions in specific dual groups are: – there is a $Λ$ (2k) set which is not $Λ (2 k + ϵ)$ in $Z (2) \oplus Z (2) \oplus \dots$ for all $2 \leq k$ , $k \in N$ and...

Bridgeland-stable moduli spaces for $K$ -trivial surfaces

Daniele Arcara, Aaron Bertram (2013)

Journal of the European Mathematical Society

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We give a one-parameter family of Bridgeland stability conditions on the derived category of a smooth projective complex surface $S$ and describe “wall-crossing behavior” for objects with the same invariants as $𝒪_{C} (H)$ when $H$ generates Pic $(S)$ and $C \in |H|$ . If, in addition, $S$ is a $K 3$ or Abelian surface, we use this description to construct a sequence of fine moduli spaces of Bridgeland-stable objects via Mukai flops and generalized elementary modifications of the universal coherent sheaf. We also discover...

Lipschitz equivalence of graph-directed fractals

Ying Xiong, Lifeng Xi (2009)

Studia Mathematica

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This paper studies the geometric structure of graph-directed sets from the point of view of Lipschitz equivalence. It is proved that if ${E_{i}}_{i}$ and ${F_{j}}_{j}$ are dust-like graph-directed sets satisfying the transitivity condition, then $E_{i ₁}$ and $E_{i ₂}$ are Lipschitz equivalent, and $E_{i}$ and $F_{j}$ are quasi-Lipschitz equivalent when they have the same Hausdorff dimension.

Biholomorphic maps determined on the boundary

Nozomu Mochizuki (1977)

Annales de l'institut Fourier

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Let $D$ be a bounded domain in $C^{n}$ such that the boundary $b D$ is topologically $S^{2 n - 1}$ in $R^{2 n}$ with a regular point; let $f : \tilde{D} \to C^{n}$ be a holomorphic map where $\tilde{D}$ is a neighborhood of $\overline{D}$ . If $f$ is one-to-one when restricted to $b D$ , then $f : D \to f (D)$ is biholomorphic.

On the structure of closed 3-manifolds

Jan Mycielski (2003)

Fundamenta Mathematicae

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We will show that for every irreducible closed 3-manifold M, other than the real projective space P³, there exists a piecewise linear map f: S → M where S is a non-orientable closed 2-manifold of Euler characteristic χ ≡ 2 (mod 3) such that $| f^{- 1} (x) | \leq 2$ for all x ∈ M, the closure of the set $x \in M : | f^{- 1} (x) | = 2$ is a cubic graph G such that $S - f^{- 1} (G)$ consists of 1/3(2-χ) + 2 simply connected regions, M - f(S) consists of two disjoint open 3-cells such that f(S) is the boundary of each of them, and f has some additional interesting...

Real singular Del Pezzo surfaces and 3-folds fibred by rational curves, II

Fabrizio Catanese, Frédéric Mangolte (2009)

Annales scientifiques de l'École Normale Supérieure

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Let $W \to X$ be a real smooth projective 3-fold fibred by rational curves such that $W (ℝ)$ is orientable. J. Kollár proved that a connected component $N$ of $W (ℝ)$ is essentially either Seifert fibred or a connected sum of lens spaces. Answering three questions of Kollár, we give sharp estimates on the number and the multiplicities of the Seifert fibres (resp. the number and the torsions of the lens spaces) when $X$ is a geometrically rational surface. When $N$ is Seifert fibred over a base orbifold $F$ , our...

Dimension vs. genus: A surface realization of the little k-cubes and an $E_{\infty}$ operad

Ralph M. Kaufmann (2009)

Banach Center Publications

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We define a new $E_{\infty}$ operad based on surfaces with foliations which contains $E_{k}$ suboperads. We construct CW models for these operads and provide applications of these models by giving actions on Hochschild complexes (thus making contact with string topology), by giving explicit cell representatives for the Dyer-Lashof-Cohen operations for the 2-cubes and by constructing new Ω spectra. The underlying novel principle is that we can trade genus in the surface representation vs. the dimension...

Stronger bounds for generalized degrees and Menger path systems

R.J. Faudree, Zs. Tuza (1995)

Discussiones Mathematicae Graph Theory

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For positive integers d and m, let $P_{d, m} (G)$ denote the property that between each pair of vertices of the graph G, there are m internally vertex disjoint paths of length at most d. For a positive integer t a graph G satisfies the minimum generalized degree condition δₜ(G) ≥ s if the cardinality of the union of the neighborhoods of each set of t vertices of G is at least s. Generalized degree conditions that ensure that $P_{d, m} (G)$ is satisfied have been investigated. In particular, it has been shown,...

Dehn twists on nonorientable surfaces

Michał Stukow (2006)

Fundamenta Mathematicae

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Let $t_{a}$ be the Dehn twist about a circle a on an orientable surface. It is well known that for each circle b and an integer n, $I (t ⁿ_{a} (b), b) = | n | I (a, b) ²$ , where I(·,·) is the geometric intersection number. We prove a similar formula for circles on nonorientable surfaces. As a corollary we prove some algebraic properties of twists on nonorientable surfaces. We also prove that if ℳ(N) is the mapping class group of a nonorientable surface N, then up to a finite number of exceptions, the centraliser of the subgroup...

On the diameter of the intersection graph of a finite simple group

Xuanlong Ma (2016)

Czechoslovak Mathematical Journal

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Let $G$ be a finite group. The intersection graph $Δ_{G}$ of $G$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper nontrivial subgroups of $G$ , and two distinct vertices $X$ and $Y$ are adjacent if $X \cap Y \neq 1$ , where $1$ denotes the trivial subgroup of order $1$ . A question was posed by Shen (2010) whether the diameters of intersection graphs of finite non-abelian simple groups have an upper bound. We answer the question and show that the diameters...

Even sets of nodes on sextic surfaces

Fabrizio Catanese, Fabio Tonoli (2007)

Journal of the European Mathematical Society

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We determine the possible even sets of nodes on sextic surfaces in $ℙ^{3}$ , showing in particular that their cardinalities are exactly the numbers in the set ${24, 32, 40, 56}$ . We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, and of homological and computer algebra on the other. We give a detailed geometric construction for the new case of an even set of 56 nodes, but the ultimate verification...

The path space of a higher-rank graph

Samuel B. G. Webster (2011)

Studia Mathematica

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We construct a locally compact Hausdorff topology on the path space of a finitely aligned k-graph Λ. We identify the boundary-path space ∂Λ as the spectrum of a commutative C*-subalgebra $D_{Λ}$ of C*(Λ). Then, using a construction similar to that of Farthing, we construct a finitely aligned k-graph Λ̃ with no sources in which Λ is embedded, and show that ∂Λ is homeomorphic to a subset of ∂Λ̃. We show that when Λ is row-finite, we can identify C*(Λ) with a full corner of C*(Λ̃), and deduce...

Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces

Mikhail Karpukhin, Gerasim Kokarev, Iosif Polterovich (2014)

Annales de l’institut Fourier

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We prove two explicit bounds for the multiplicities of Steklov eigenvalues $σ_{k}$ on compact surfaces with boundary. One of the bounds depends only on the genus of a surface and the index $k$ of an eigenvalue, while the other depends as well on the number of boundary components. We also show that on any given Riemannian surface with smooth boundary the multiplicities of Steklov eigenvalues $σ_{k}$ are uniformly bounded in $k$ .

Displaying similar documents to “A continuous Helson surface in 𝐑 3 ”

Displaying similar documents to “A continuous Helson surface in $𝐑^{3}$ ”