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Let ${𝙴𝙼𝙱𝙴𝙳}_{k \to d}$ be the following algorithmic problem: Given a ﬁnite simplicial complex $K$ of dimension at most $k$ , does there exist a (piecewise linear) embedding of $K$ into $ℝ^{d}$ ? Known results easily imply polynomiality of ${𝙴𝙼𝙱𝙴𝙳}_{k \to 2}$ ( $k = 1, 2$ ; the case $k = 1, d = 2$ is graph planarity) and of ${𝙴𝙼𝙱𝙴𝙳}_{k \to 2 k}$ for all $k \geq 3$ . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that ${𝙴𝙼𝙱𝙴𝙳}_{d \to d}$ and ${𝙴𝙼𝙱𝙴𝙳}_{(d - 1) \to d}$ are undecidable for each $_{d} \geq 5$ . Our main result is NP-hardness of ${𝙴𝙼𝙱𝙴𝙳}_{2 \to 4}$ and, more generally, of ${𝙴𝙼𝙱𝙴𝙳}_{k \to d}$ for all $k$ , $d$ with...

Hauptvermutung et triangulation des variétés

Claude Morlet (1968/1969)

Séminaire Bourbaki

h-Cobordismes entre variétés homéomorphes.

Jean-Claude Hausmann (1975)

Commentarii mathematici Helvetici

h-cobordisms between 1-connected 4-manifolds.

Kreck, Matthias (2001)

Geometry & Topology

Heegaard and regular genus of 3-manifolds with boundary.

P. Cristofori, C. Gagliardi, L. Grasselli (1995)

Revista Matemática de la Universidad Complutense de Madrid

By means of branched coverings techniques, we prove that the Heegaard genus and the regular genus of an orientable 3-manifold with boundary coincide.

Heegaard splittings of Seifert fibered spaces.

Yoav Moriah (1988)

Inventiones mathematicae

Heegaard splittings of (surface) x I are standars.

Martin Scharlemann, Abigail Thompson (1993)

Mathematische Annalen

Heegard and regular genus agree for compact $3$ -manifolds

Paola Cristofori (1998)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

Hermitian forms on link modules.

M. Farber (1991)

Commentarii mathematici Helvetici

High-dimensional knots corresponding to the fractional Fibonacci groups

Andrzej Szczepański, Andreĭ Vesnin (1999)

Fundamenta Mathematicae

We prove that the natural HNN-extensions of the fractional Fibonacci groups are the fundamental groups of high-dimensional knot complements. We also give some characterization and interpretation of these knots. In particular we show that some of them are 2-knots.

Higher dimensional simple knots and minimal Seifert surfaces.

Eva Bayer-Fluckiger (1983)

Commentarii mathematici Helvetici

Homogeneity of dynamically defined wild knots.

Gabriela Hinojosa, Alberto Verjovsky (2006)

Revista Matemática Complutense

In this paper we prove that a wild knot K which is the limit set of a Kleinian group acting conformally on the unit 3-sphere, with its standard metric, is homogeneous: given two points p, q ∈ K, there exists a homeomorphism f of the sphere such that f(K) = K and f(p) = q. We also show that if the wild knot is a fibered knot then we can choose an f which preserves the fibers.

Currently displaying 181 – 200 of 507

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Displaying 181 – 200 of 507

Geometrie Classification of Simplicial Structures on Topologieal Manifolds.

Géométrie systolique des variétés de groupe fondamental $𝐙^{2}$

Grothendieck Groups of Sesquilinear Forms over a Ring with Involution.

Groups of piecewise linear homeomorphisms of the real line.

Handle-decompositions of $P L$ $4$ -manifolds

Hardness of embedding simplicial complexes in $ℝ^{d}$

Hauptvermutung et triangulation des variétés

h-Cobordismes entre variétés homéomorphes.

h-cobordisms between 1-connected 4-manifolds.

Heegaard and regular genus of 3-manifolds with boundary.

Heegaard splittings of Seifert fibered spaces.

Heegaard splittings of (surface) x I are standars.

Heegard and regular genus agree for compact $3$ -manifolds

Hermitian forms on link modules.

High-dimensional knots corresponding to the fractional Fibonacci groups

Higher dimensional simple knots and minimal Seifert surfaces.

Homogeneity of dynamically defined wild knots.

Homotopie des espaces de concordances

Homotopy characterization of weakly flat knots

Homotopy Lie algebras; lower central series and the Koszul property.

Currently displaying 181 – 200 of 507