Morin singularities of collections of one-forms and vector fields

Camila M. Ruiz

Journal of Singularities
volume 22 (2020), 278-314

Received: 1 March 2019. Received in revised form: 16 February 2020.

DOI: 10.5427/jsing.2020.22r

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Abstract:

Inspired by the properties of a collection of n gradient vector fields \nabla f_1, ..., \nabla f_n from a Morin map f=(f_1,...,f_n): M -> R^n$, with dim M ≥ n, we introduce the notion of Morin singularities in the context of collections of one-forms and collections of vector fields. We also study the singularities of generic one-forms which are related to specific collections (Morin collections) and we generalize a result of T. Fukuda on Euler characteristic for the case of collections of one-forms and vector fields.

2010 Mathematical Subject Classification:

Primary 57R45; Secondary 57R70, 58K45

Key words and phrases:

Morin singularities, collections of vector fields, collections of one-forms, critical locus

Author(s) information:

Camila M. Ruiz
Departamento de Matemática Aplicada
Instituto de Ciências Tecnológias e Exatas
Universidade Federal do Triângulo Mineiro
38064-200 Uberaba - MG, Brasil
email: camila.ruiz@uftm.edu.br