A primary obstruction to topological embeddings between generalized manifolds

• Grant number: 24/06290-5
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: September 01, 2024
• End date: February 28, 2025
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Edivaldo Lopes dos Santos
• Grantee: Odete Lara Melo Budtinger
• Supervisor: Osamu Saeki
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Kyushu University, Japan
• Associated to the scholarship: 23/01101-7 - Primary obstruction to topological embeddings between manifolds, BP.MS

Abstract

This project aims to present a study about a determined class of primary obstruction to the existence of a homotopy between a function $f$ and a topological embedding into generalized manifolds. This project complements the master's scholarship project Fapesp Process 2023/01101-7, considering the results for generalized manifolds and some additional properties and applications. Such class is homotopically invariant and can be studied in a point of view of Algebraic Topology, without differentiability in the involved spaces.