Handle-decompositions of -manifolds
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Maria Rita Casali, Luca Malagoli (1997)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
Jiří Matoušek, Martin Tancer, Uli Wagner (2011)
Journal of the European Mathematical Society
Let be the following algorithmic problem: Given a finite simplicial complex of dimension at most , does there exist a (piecewise linear) embedding of into ? Known results easily imply polynomiality of (; the case is graph planarity) and of for all . We show that the celebrated result of Novikov on the algorithmic unsolvability of recognizing the 5-sphere implies that and are undecidable for each . Our main result is NP-hardness of and, more generally, of for all , with...
Claude Morlet (1968/1969)
Séminaire Bourbaki
Jean-Claude Hausmann (1975)
Commentarii mathematici Helvetici
Kreck, Matthias (2001)
Geometry & Topology
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.
Yoav Moriah (1988)
Inventiones mathematicae
Martin Scharlemann, Abigail Thompson (1993)
Mathematische Annalen
Paola Cristofori (1998)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
M. Farber (1991)
Commentarii mathematici Helvetici
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.
Eva Bayer-Fluckiger (1983)
Commentarii mathematici Helvetici
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.
Jean-Louis Loday (1977/1978)
Séminaire Bourbaki
Vo-Thanh Liem (1979)
Fundamenta Mathematicae
Papadima, Stefan, Suciu, Alexander I. (2004)
Geometry & Topology
W. Balcerak, B. Hajduk (1981)
Colloquium Mathematicae
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.
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