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Extensions through codimension one to sense preserving mappings

Charles J. Titus (1973)

Annales de l'institut Fourier

The archetype for the questions considered is: “Which plane oriented curves in the plane are representable as the images of the boundary of a disk under holomorphic function?” This question is equivalent to: “Which immersion of the circle in the plane are extendable to smooth sense preserving (= non-negative jacobian) mappings of the closed disk with the jacobian positive on the boundary?”The second question is generalized in terms of the genus and dimension of the source and target. An exposition...

Géométries modèles de dimension trois

Yves de Cornulier (2008/2009)

Séminaire de théorie spectrale et géométrie

On expose une preuve détaillée de la classification par Thurston des huit géométries modèles de dimension trois.

Hyperbolic knots and cyclic branched covers.

Luisa Paoluzzi (2005)

Publicacions Matemàtiques

We collect several results on the determination of hyperbolic knots by means of their cyclic branched covers. We construct examples of knots having two common cyclic branched covers. Finally, we briefiy discuss the problem of determination of hyperbolic links.

Infinite group actions on spheres.

Gaven J. Martin (1988)

Revista Matemática Iberoamericana

This paper is mainly intended as a survey of the recent work of a number of authors concerning certain infinite group actions on spheres and to raise some as yet unanswered questions. The main thrust of the current research in this area has been to decide what topological and geometrical properties characterise the infinite conformal or Möbius groups. One should then obtain reasonable topological or geometrical restrictions on a subgroup G of the homeomorphism group of a sphere which will imply...

Introduction to the basics of Heegaard Floer homology

Bijan Sahamie (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

This paper provides an introduction to the basics of Heegaard Floer homology with some emphasis on the hat theory and to the contact geometric invariants in the theory. The exposition is designed to be comprehensible to people without any prior knowledge of the subject.

Jones polynomials, volume and essential knot surfaces: a survey

David Futer, Efstratia Kalfagianni, Jessica S. Purcell (2014)

Banach Center Publications

This paper is a brief overview of recent results by the authors relating colored Jones polynomials to geometric topology. The proofs of these results appear in the papers [18, 19], while this survey focuses on the main ideas and examples.


Slavik Jablan, Radmila Sazdanović (2007)

Visual Mathematics

On stability of Alexander polynomials of knots and links (survey)

Mikami Hirasawa, Kunio Murasugi (2014)

Banach Center Publications

We study distribution of the zeros of the Alexander polynomials of knots and links in S³. After a brief introduction of various stabilities of multivariate polynomials, we present recent results on stable Alexander polynomials.

Some topics concerning homeomorphic parameterizations.

Stephen Semmes (2001)

Publicacions Matemàtiques

In this survey, we consider several questions pertaining to homeomorphisms, including criteria for their existence in certain circumstances, and obstructions to their existence.

The Nash-Kuiper process for curves

Vincent Borrelli, Saïd Jabrane, Francis Lazarus, Boris Thibert (2011/2012)

Séminaire de théorie spectrale et géométrie

A strictly short embedding is an embedding of a Riemannian manifold into an Euclidean space that strictly shortens distances. From such an embedding, the Nash-Kuiper process builds a sequence of maps converging toward an isometric embedding. In that paper, we describe this Nash-Kuiper process in the case of curves. We state an explicit formula for the limit normal map and perform its Fourier series expansion. We then adress the question of Holder regularity of the limit map.

Traces, lengths, axes and commensurability

Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

The focus of this paper are questions related to how various geometric and analytical properties of hyperbolic 3-manifolds determine the commensurability class of such manifolds. The paper is for the large part a survey of recent work.

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