Geodesic
Global classification of isolated singularities in dimensions (4,3) and (8,5)
Funar, Louis1 
1 Institut Fourier BP 74 UMR 5582 Université de Grenoble 38402 Saint-Martin-d’Hères cedex, France
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 4, pp. 819-861

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We characterize those closed 2k-manifolds admitting smooth maps into (k+1)-manifolds with only finitely many critical points, for k∈{2,4}. We compute then the minimal number of critical points of such smooth maps for k=2 and, under some fundamental group restrictions, also for k=4. The main ingredients are King’s local classification of isolated singularities, decomposition theory, low dimensional cobordisms of spherical fibrations and 3-manifolds topology.

Publié le :
Classification : 57R45, 58K05, 57R60, 57R70

Funar, Louis 1

1 Institut Fourier BP 74 UMR 5582 Université de Grenoble 38402 Saint-Martin-d’Hères cedex, France 
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     title = {Global classification of isolated singularities in dimensions (4,3) and (8,5)},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Funar, Louis. Global classification of isolated singularities in dimensions (4,3) and (8,5). Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 4, pp. 819-861. http://geodesic.mathdoc.fr/item/ASNSP_2011_5_10_4_819_0/