Observations on the 'span' of certain classes of varieties

Author(s)

Matheus Eduardo Dametto Silva

• Document type: Master's Dissertation
• Press: São José do Rio Preto. 2022-07-21.
• Institution: Universidade Estadual Paulista (Unesp). Instituto de Biociências Letras e Ciências Exatas. São José do Rio Preto
• Defense date: 2022-02-21
• Advisor: Alice Kimie Miwa Libardi

Abstract

The purpose of this dissertation is to present the part of the P. Sanrakaran article [14], where the problem of vector fields for homogeneous spaces is widely discussed. The span of a smooth manifold M is defined to be the greatest natural r such that there are linearly independent vector fields at all points of the manifold. Based on some results and examples, our goal will be to determine the span (M), or to get a good approximation for it. In particular, we will work on Stiefel Manifolds and the Projective of Stiefel Manifolds. We present some conjectures proposed by J. Korbas and P. Zvengrowski in the article [6]. For the discussion to be possible, a preliminary study of relevant concepts for the understanding and evaluation of this theme will be necessary, such as some concepts of Algebraic Topology, smooth manifolds, vector bundles and characteristic classes. (AU)

• FAPESP's process: 20/00814-1 - The study of the vector field problem for homogeneous spaces
• Grantee: Matheus Eduardo Dametto Silva
• Support Opportunities: Scholarships in Brazil - Master