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.

We characterize those closed $2k$-manifolds admitting smooth maps into $\left(k+1\right)$-manifolds with only finitely many critical points, for $k\in \left\{2,4\right\}$. 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 : 2018-06-21
Classification : 57R45,  58K05,  57R60,  57R70
@article{ASNSP_2011_5_10_4_819_0,
author = {Funar, Louis},
title = {Global classification of isolated singularities in dimensions (4,3) and (8,5)},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {819--861},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 10},
number = {4},
year = {2011},
zbl = {1241.57037},
mrnumber = {2932895},
language = {en},
url = {archive.numdam.org/item/ASNSP_2011_5_10_4_819_0/}
}
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://archive.numdam.org/item/ASNSP_2011_5_10_4_819_0/

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