For 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.

Covering numbers of manifolds and critical points of a Morse function / Cavicchioli, Alberto. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - STAMPA. - 70:(1990), pp. 279-304.

Covering numbers of manifolds and critical points of a Morse function

CAVICCHIOLI, Alberto
1990

Abstract

For 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.
70
279
304
Covering numbers of manifolds and critical points of a Morse function / Cavicchioli, Alberto. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - STAMPA. - 70:(1990), pp. 279-304.
Cavicchioli, Alberto
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/451016
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