Involutions of 3-dimensional handlebodies

Andrea Pantaleoni; Riccardo Piergallini

Displaying similar documents to “Involutions of 3-dimensional handlebodies”

Lifting of homeomorphisms to branched coverings of a disk

Bronisław Wajnryb, Agnieszka Wiśniowska-Wajnryb (2012)

Fundamenta Mathematicae

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We consider a simple, possibly disconnected, d-sheeted branched covering π of a closed 2-dimensional disk D by a surface X. The isotopy classes of homeomorphisms of D which are pointwise fixed on the boundary of D and permute the branch values, form the braid group Bₙ, where n is the number of branch values. Some of these homeomorphisms can be lifted to homeomorphisms of X which fix pointwise the fiber over the base point. They form a subgroup $L^{π}$ of finite index in Bₙ. For each equivalence...

Erratum to the paper "On the disc theorem" (Ann. Polon. Math. 55 (1991), 1-10)

Cabiria Andreian Cazacu (1992)

Annales Polonici Mathematici

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Due to a technical error, part of a sentence was omitted on the top of page 8. The first line should read: “where $f_{p}^{k}$ , $p = a_{l}$ or $b_{l}$ , means the number of folds of the covering $(δ_{k}^{''}, T |, Δ_{l}^{''})$ ending at p, i.e. covering a neighbourhood of p in $a_{l} b_{l}$ without covering p itself”.

On Ponomarev-Systems

Ying Ge, Lin Shou (2007)

Bollettino dell'Unione Matematica Italiana

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In this paper the relations of mappings and families of subsets are investigated in Ponomarev-systems, and the following results are obtained. (1) $f$ is a sequence-covering (resp. 1-sequence-covering) mapping iff $\mathcal{P}$ is a csf -network (resp. snf -network) of $X$ for a Ponomarev-system $(f,M,X,\mathcal{P})$ ; (2) $f$ is a sequence-covering (resp. 1-sequence-covering) mapping iff every $\mathcal{P}_{n}$ is a cs-cover (resp. wsn-cover) of $X$ for a Ponomarev-system $(f,M,X,\{\mathcal{P}_{n}\})$ . As applications of these results, some relations between sequence-covering...

On surfaces with p $_{𝑔}$ = q = 1 and non-ruled bicanonical involution

Carlos Rito (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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This paper classifies surfaces $S$ of general type with $p_{g} = q = 1$ having an involution $i$ such that $S / i$ has non-negative Kodaira dimension and that the bicanonical map of $S$ factors through the double cover induced by $i .$ It is shown that $S / i$ is regular and either: a) the Albanese fibration of $S$ is of genus 2 or b) $S$ has no genus 2 fibration and $S / i$ is birational to a $K 3$ surface. For case a) a list of possibilities and examples are given. An example for case b) with $K^{2} = 6$ is also constructed.

Irreducibility of Hurwitz Spaces of Coverings with Monodromy Groups Weyl Groups of Type $W(B_{d})$

Francesca Vetro (2007)

Bollettino dell'Unione Matematica Italiana

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Let Y be a smooth, connected, projective complex curve of genus > = 0. Biggers and Fried proved the irreducibility of the Hurwitz spaces which parametrize coverings of $P^{1}$ whose monodromy group is a Weyl of type $W(B_{d})$ . Here we prove the irreducibility of Hurwitz spaces that parametrize coverings of Y with monodromy group a Weyl group of type $W(B_{d})$ .

The covering number for category and partition relations on $P_{ω} (λ)$

Pierre Matet (2002)

Fundamenta Mathematicae

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We show that cov(M) is the least infinite cardinal λ such that $P_{ω} (λ)$ (the set of all finite subsets of λ ) fails to satisfy a certain natural generalization of Ramsey’s Theorem.

Connected Components of Hurwitz Spaces of Coverings with One Special Fiber and Monodromy Groups Contained in a Weyl Group of Type $B_{d}$

Francesca Vetro (2008)

Bollettino dell'Unione Matematica Italiana

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Let $X$ , $X^{\prime}$ , $Y$ be smooth projective complex curves with $Y$ curve of genus $\geq 1$ . Let $d$ be an integer $\geq 3$ , let $\underline{e}=(e_{1},\ldots,e_{r})$ be a partition of $d$ and let $|e|=\sum_{i=1}^{r}(e_{i}-1)$ . Let $X\xrightarrow{\pi}X^{\prime}\xrightarrow{f}Y$ be a sequence of coverings where $\pi$ is a degree 2 branched covering and $f$ is a degree $d$ covering, with monodromy group $S_{d}$ , branched in $n_{2}+1$ points, one of which is special point $c$ whose local monodromy has cycle type given by $\underline{e}$ . Moreover the branch locus of the covering $\pi$ is contained in $f^{-1}(c)$ . In this paper we prove the irreducibility...

Universal embeddings of $l^{1} (α)$ into the space of continuous functions on a product space

N. Kalamidas, Th. Zachariades (1989)

Colloquium Mathematicae

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Effective decomposition of σ-continuous Borel functions

Gabriel Debs (2014)

Fundamenta Mathematicae

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We prove that if a Δ¹₁ function f with Σ¹₁ domain X is σ-continuous then one can find a Δ¹₁ covering ${(A ₙ)}_{n \in ω}$ of X such that $f_{| A ₙ}$ is continuous for all n. This is an effective version of a recent result by Pawlikowski and Sabok, generalizing an earlier result of Solecki.

Embedding in $T_{3}$ - $F_{σ}$ spaces

D. W. Hajek, I. Irizarry (1981)

Matematički Vesnik

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Effective bounds for Faltings’s delta function

Jay Jorgenson, Jürg Kramer (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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In his seminal paper on arithmetic surfaces Faltings introduced a new invariant associated to compact Riemann surfaces $X$ , nowadays called Faltings’s delta function and here denoted by $δ_{Fal} (X)$ . For a given compact Riemann surface $X$ of genus $g_{X} = g$ , the invariant $δ_{Fal} (X)$ is roughly given as minus the logarithm of the distance with respect to the Weil-Petersson metric of the point in the moduli space $ℳ_{g}$ of genus $g$ curves determined by $X$ to its boundary $\partial ℳ_{g}$ . In this paper we begin by revisiting a formula derived...

Addendum to “On the $p^{λ}$ problem”

Stephan Baier (2005)

Acta Arithmetica

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A curve of genus $q$ with a Half-Canonical embedding in $\mathbf{P}^{3}$

Sevin Recillas (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si costruiscono curve di genere $g=4n—3$ , $n\geq 3$ che hanno $2^{n-3}(2^{n-2}-1)$ fasci semicanonici $L$ tali che $h^{0}(L)=4$ . Per $n+3$ si dimostra che gli $L$ sono molto ampi.

On covering and quasi-unsplit families of curves

Laurent Bonavero, Cinzia Casagrande, Stéphane Druel (2007)

Journal of the European Mathematical Society

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Given a covering family $V$ of effective 1-cycles on a complex projective variety $X$ , we find conditions allowing one to construct a geometric quotient $q : X \to Y$ , with $q$ regular on the whole of $X$ , such that every fiber of $q$ is an equivalence class for the equivalence relation naturally defined by $V$ . Among other results, we show that on a normal and $ℚ$ -factorial projective variety $X$ with canonical singularities and $dim X \leq 4$ , every covering and quasi-unsplit family $V$ of rational curves generates a geometric...

The general methods of finding the sum $S_{n}$ for all kinds of series, II

K. Orlov (1981)

Matematički Vesnik

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An effective proof of the hyperelliptic Shafarevich conjecture

Rafael von Känel (2014)

Journal de Théorie des Nombres de Bordeaux

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Let $C$ be a hyperelliptic curve of genus $g \geq 1$ over a number field $K$ with good reduction outside a finite set of places $S$ of $K$ . We prove that $C$ has a Weierstrass model over the ring of integers of $K$ with height effectively bounded only in terms of $g$ , $S$ and $K$ . In particular, we obtain that for any given number field $K$ , finite set of places $S$ of $K$ and integer $g \geq 1$ one can in principle determine the set of $K$ -isomorphism classes of hyperelliptic curves over $K$ of genus $g$ with good reduction outside...

A characterization of the disc $D^{n}$

Th. Friedrich (1974)

Colloquium Mathematicae

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On the strongly ambiguous classes of some biquadratic number fields

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous (2016)

Mathematica Bohemica

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We study the capitulation of $2$ -ideal classes of an infinite family of imaginary bicyclic biquadratic number fields consisting of fields $𝕜 = ℚ (\sqrt{2 p q}, i)$ , where $i = \sqrt{- 1}$ and $p \equiv - q \equiv 1 (mod 4)$ are different primes. For each of the three quadratic extensions $𝕂 / 𝕜$ inside the absolute genus field $𝕜^{(*)}$ of $𝕜$ , we determine a fundamental system of units and then compute the capitulation kernel of $𝕂 / 𝕜$ . The generators of the groups ${Am}_{s} (𝕜 / F)$ and $Am (𝕜 / F)$ are also determined from which we deduce that $𝕜^{(*)}$ is smaller than the relative genus field ${(𝕜 / ℚ (i))}^{*}$ . Then we prove...

Singularities of $2 Θ$ -divisors in the jacobian

Christian Pauly, Emma Previato (2001)

Bulletin de la Société Mathématique de France

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We consider the linear system $| 2 Θ_{0} |$ of second order theta functions over the Jacobian $J C$ of a non-hyperelliptic curve $C$ . A result by J.Fay says that a divisor $D \in | 2 Θ_{0} |$ contains the origin $𝒪 \in J C$ with multiplicity $4$ if and only if $D$ contains the surface $C - C = {𝒪 (p - q) ∣ p, q \in C} \subset J C$ . In this paper we generalize Fay’s result and some previous work by R.C.Gunning. More precisely, we describe the relationship between divisors containing $𝒪$ with multiplicity $6$ , divisors containing the fourfold $C_{2} - C_{2} = {𝒪 (p + q - r - s) ∣ p, q, r, s \in C}$ , and divisors singular along $C - C$ , using...