All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 18 of 18

Showing per page

Hardness of embedding simplicial complexes in ℝ d

Jiří Matoušek, Martin Tancer, Uli Wagner (2011)

Journal of the European Mathematical Society

Let 𝙴𝙼𝙱𝙴𝙳 k → 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 → 2 ( k = 1 , 2 ; the case k = 1 , d = 2 is graph planarity) and of 𝙴𝙼𝙱𝙴𝙳 k → 2 k for all k ≥ 3 . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that 𝙴𝙼𝙱𝙴𝙳 d → d and 𝙴𝙼𝙱𝙴𝙳 ( d - 1 ) → d are undecidable for each d ≥ 5 . Our main result is NP-hardness of 𝙴𝙼𝙱𝙴𝙳 2 → 4 and, more generally, of 𝙴𝙼𝙱𝙴𝙳 k → d for all k , d with...

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.

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.

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.

Hyperspaces of CW-complexes

Bao-Lin Guo, Katsuro Sakai (1993)

Fundamenta Mathematicae

It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.

Currently displaying 1 – 18 of 18

Page 1