1,721,112 research outputs found
Pseudo-dissezioni e triangolazioni contratte di spazi con singolarita` isolate
No full textI prove a theorem of contracted triangulation for spaces with "few" points of singularity. These spaces with PL maps form a Category that contains the Category of PL manifolds. Then I prove some theorems of characterization and comparison among the new introduced spaces and the classically well known spaces
A genus for n-dimensional knots and links
No full textWe introduce the concept of regular genus for n-dimensional links and knots, and study the topological properties of it. Some characterization theorems of the trivial knot are given. In particular, the only genus zero n-dimensional knot is proved to be homeomorphic with the trivial knot. Then the regular genus of a knot is proved to be related to the one-dimensional homology of the universal abelian covering of its complement. Some applications to low-dimensional links and a final section about connected sums of links complete the paper
Manici e fattorizzazioni delle trivarieta`
No full textIn questa nota si presenta una breve dimostrazione (di carattere topologico) del teorema di riconoscimento dei manici combinatori nell'ambito dei grafi 4-colorati sugli spigoli
Finding nice crystallizations for handle free n-manifolds
No full textThe paper deals with combinatorial structures (pseudo-complexes, crystallizations) giving a direct link between the topology of triangulated manifolds and the theory of edge-colored multigraphs. We define the concept of regular crystallization of a manifold and prove that every non-trivial handle free closed n-manifold has a regular crystallization. Then we study some applications of regular crystallizations and give a counter-example to a conjecture of Y. Tsukui about strong frames of the 3-sphere
Lins-Mandel 3-manifolds and their groups: a simple proof of the homology sphere conjecture
No full textThe Lins-Mandel manifolds are combinatorially represented by a 4-parametric family of colored graphs S(n,\ell,t,c) defined in Discrete Math. 57 (1985). In the present paper we obtain a finite presentation of the fundamental group of such manifolds for t = \ell -1 and c=1. As a consequence, the homology sphere conjecture 2, stated in the quoted paper, can be easily proved by a direct algebraic calculus on the homology groups
Covering numbers of manifolds and critical points of a Morse function
No full textFor a closed connected triangulated n-manifold M, we study some numerical invariants (named category and covering numbers) of M which are strictly related to the topological structure of M. We complete the classical results of 3-manifold topology and then we prove some characterization theorems in higher dimensions. Finally, some applications are given about the minimal number of critical points (resp. values) of Morse functions defined on a closed connected smooth n-manifold
Mobius transformations and surface groups
No full textWe describe a simple geometric construction of the fundamental group of the closed connected orientable surface of genus g (g greater or equal 2) presented in terms of 2g complex Mobius transformations as generators and of one relation among them. Our construction allows us to write the equation of any transformation of the above group. Finally, we give a recurrence formula to obtain all the vertices of the tessellation induced by the above group in the open unit disc endowed by the hyperbolic metric
Neuwirth manifolds and colourings of graphs
No full textWe use the representation of PL manifolds via graphs with colored edges. Then we describe a very fast construction to obtain a 4-colored graph representing a closed orientable 3-manifold from its Heegaard diagram. This construction allows us to completely classify a countable class of closed orientable 3-manifolds introduced by L. Neuwirth in Proc. Camb. Phil. Soc. 64 (1968)
Una rappresentazione delle trivarieta` orientabili mediante atlanti minimali di superficie
No full textA representation theorem for orientable closed 3-manifolds is proved. Some applications about lens spaces, 3-manifolds of genus two, and connected sums are studied
A new handlebody decomposition of 3-manifolds with connected boundary and their fundamental group
No full textWe give a new theorem of handlebody decomposition for compact 3-manifolds with connected boundary. The decomposition type, given here, allows us to calculate with great facility a presentation of the fundamental group of a 3-manifold with connected boundary
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