Given a connected compact n-manifold M, a natural invariant of M is the minimal number of balls which are needed to cover M. If the intersection of any number of balls has again balls as connected components, we get the notion of ball-intersection atlas of M. We prove that each minimal ball-intersection atlas of a connected piecewise-linear n-manifold M has exactly n balls if the boundary of M is non-void.

Minimal atlases of manifolds / Cavicchioli, Alberto; Grasselli, Luigi. - In: CAHIERS DE TOPOLOGIE ET GÉOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES. - ISSN 1245-530X. - STAMPA. - 26 (4):(1985), pp. 389-397.

Minimal atlases of manifolds

CAVICCHIOLI, Alberto;GRASSELLI, Luigi
1985

Abstract

Given a connected compact n-manifold M, a natural invariant of M is the minimal number of balls which are needed to cover M. If the intersection of any number of balls has again balls as connected components, we get the notion of ball-intersection atlas of M. We prove that each minimal ball-intersection atlas of a connected piecewise-linear n-manifold M has exactly n balls if the boundary of M is non-void.
26 (4)
389
397
Minimal atlases of manifolds / Cavicchioli, Alberto; Grasselli, Luigi. - In: CAHIERS DE TOPOLOGIE ET GÉOMÉTRIE DIFFÉRENTIELLE CATÉGORIQUES. - ISSN 1245-530X. - STAMPA. - 26 (4):(1985), pp. 389-397.
Cavicchioli, Alberto; Grasselli, Luigi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/451024
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