Quandle coverings and their Galois correspondence

Michael Eisermann

Displaying similar documents to “Quandle coverings and their Galois correspondence”

Two classes of almost Galois coverings for algebras

Piotr Dowbor, Adam Hajduk (2012)

Colloquium Mathematicae

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We prove that for any representation-finite algebra A (in fact, finite locally bounded k-category), the universal covering F: Ã → A is either a Galois covering or an almost Galois covering of integral type, and F admits a degeneration to the standard Galois covering F̅: Ã→ Ã/G, where $G = Π (Γ_{A})$ is the fundamental group of $Γ_{A}$ . It is shown that the class of almost Galois coverings F: R → R’ of integral type, containing the series of examples from our earlier paper [Bol. Soc. Mat. Mexicana 17 (2011)],...

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”.

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.

Involutions of 3-dimensional handlebodies

Andrea Pantaleoni, Riccardo Piergallini (2011)

Fundamenta Mathematicae

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We study the orientation preserving involutions of the orientable 3-dimensional handlebody $H_{g}$ , for any genus g. A complete classification of such involutions is given in terms of their fixed points.

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...

Some topological properties of $ω$ -covering sets

Andrzej Nowik (2000)

Czechoslovak Mathematical Journal

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We prove the following theorems: There exists an $ω$ -covering with the property $s_{0}$ . Under $c o v (𝒩) =$ there exists $X$ such that $\forall_{B \in ℬ o r} [B \cap X$ is not an $ω$ -covering or $X ∖ B$ is not an $ω$ -covering]. Also we characterize the property of being an $ω$ -covering.

Algebraic $K$ -theory of the first Morava $K$ -theory

Christian Ausoni, John Rognes (2012)

Journal of the European Mathematical Society

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For a prime $p \geq 5$ , we compute the algebraic $K$ -theory modulo $p$ and $v_{1}$ of the mod $p$ Adams summand, using topological cyclic homology. On the way, we evaluate its modulo $p$ and $v_{1}$ topological Hochschild homology. Using a localization sequence, we also compute the $K$ -theory modulo $p$ and $v_{1}$ of the first Morava $K$ -theory.

Noncommutative numerical motives, Tannakian structures, and motivic Galois groups

Matilde Marcolli, Gonçalo Tabuada (2016)

Journal of the European Mathematical Society

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In this article we further the study of noncommutative numerical motives, initiated in [30, 31]. By exploring the change-of-coefficients mechanism, we start by improving some of the main results of [30]. Then, making use of the notion of Schur-finiteness, we prove that the category NNum ${(k)}_{F}$ of noncommutative numerical motives is (neutral) super-Tannakian. As in the commutative world, NNum ${(k)}_{F}$ is not Tannakian. In order to solve this problem we promote periodic cyclic homology to a well-defined...

A new lower bound for the football pool problem for $7$ matches

Laurent Habsieger (1996)

Journal de théorie des nombres de Bordeaux

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Let $K_{3} (7, 1)$ denote the minimum cardinality of a ternary code of length $7$ and covering radius one. In a previous paper, we improved on the lower bound $K_{3} (7, 1) \geq 147$ by showing that $K_{3} (7, 1) \geq 150$ . In this note, we prove that $K_{3} (7, 1) \geq 153$ .

On star covering properties related to countable compactness and pseudocompactness

Marcelo D. Passos, Heides L. Santana, Samuel G. da Silva (2017)

Commentationes Mathematicae Universitatis Carolinae

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We prove a number of results on star covering properties which may be regarded as either generalizations or specializations of topological properties related to the ones mentioned in the title of the paper. For instance, we give a new, entirely combinatorial proof of the fact that $Ψ$ -spaces constructed from infinite almost disjoint families are not star-compact. By going a little further we conclude that if $X$ is a star-compact space within a certain class, then $X$ is neither first countable...

Explicit Selmer groups for cyclic covers of ℙ¹

Michael Stoll, Ronald van Luijk (2013)

Acta Arithmetica

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For any abelian variety J over a global field k and an isogeny ϕ: J → J, the Selmer group $S e l^{ϕ} (J, k)$ is a subgroup of the Galois cohomology group $H ¹ (G a l (k^{s} / k), J [ϕ])$ , defined in terms of local data. When J is the Jacobian of a cyclic cover of ℙ¹ of prime degree p, the Selmer group has a quotient by a subgroup of order at most p that is isomorphic to the ‘fake Selmer group’, whose definition is more amenable to explicit computations. In this paper we define in the same setting the ‘explicit Selmer group’, which...

Random Galois extensions of Hilbertian fields

Lior Bary-Soroker, Arno Fehm (2013)

Journal de Théorie des Nombres de Bordeaux

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Let $L$ be a Galois extension of a countable Hilbertian field $K$ . Although $L$ need not be Hilbertian, we prove that an abundance of large Galois subextensions of $L / K$ are.

Fermat numbers and integers of the form $a^{k} + a^{l} + p^{α}$

Yong-Gao Chen, Rui Feng, Nicolas Templier (2008)

Acta Arithmetica

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On signatures associated with ramified coverings and embedding problems

J. Wood, Emery Thomas (1973)

Annales de l'institut Fourier

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Given a cohomology class $ξ \in H^{2} (M; Z)$ there is a smooth submanifold $K \subset M$ Poincaré dual to $ξ$ . A special class of such embeddings is characterized by topological properties which hold for nonsingular algebraic hypersurfaces in $C P_{n}$ . This note summarizes some results on the question: how does the divisibility of $ξ$ restrict the dual submanifolds $K$ in this class ? A formula for signatures associated with a $d$ -fold ramified cover of $M$ branched along $K$ is given and a proof is included in case $d = 2$ .

Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers

Robert Lipshitz, David Treumann (2016)

Journal of the European Mathematical Society

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Let $A$ be a dg algebra over $𝔽_{2}$ and let $M$ be a dg $A$ -bimodule. We show that under certain technical hypotheses on $A$ , a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product $M \otimes_{A}^{L} M$ and converges to the Hochschild homology of $M$ . We apply this result to bordered Heegaard Floer theory, giving spectral sequences associated to Heegaard Floer homology groups of certain branched and unbranched double covers.