Characteristic classes and intersection homology

• Grant number: 15/06697-9
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 03, 2015
• End date: August 02, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: João Carlos Ferreira Costa
• Grantee: João Carlos Ferreira Costa
• Visiting researcher: Jean-Paul Michel Ildephonse Brasselet
• Visiting researcher institution: Institut de Mathématiques de Luminy, France
• Host Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
• Associated research grant: 14/00304-2 - Singularities of differentiable mappings: theory and applications, AP.TEM

Abstract

The research project is on the characteristic classes and intersection homology theory. The first subject to be investigated concerns Milnor classes. It is curious that, at the moment, there are few (or none) examples and applications of them. Another point on Milnor classes, is that the Prof. Brasselet gave a conjecture formula for duality of these classes in terms of polar varieties. Now, it is expected to explicit the proof of this conjecture. Another part of this project is to provide a geometric representation of cicles permited in intersection homology theory. (AU)

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BRASSELET, JEAN-PAUL; CHACHAPOYAS, NANCY; RUAS, MARIA A. S.. Generic sections of essentially isolated determinantal singularities. INTERNATIONAL JOURNAL OF MATHEMATICS, v. 28, n. 11, OCT 2017. (15/06697-9, 10/09736-1, 14/00304-2, 11/20082-6)

BRASSELET, JEAN-PAUL; SUWA, TATSUO. Local and global coincidence homology classes. Journal of Fixed Point Theory and Applications, v. 23, n. 2, MAY 2021. (15/06697-9)

BRASSELET, JEAN-PAUL; CORREA, MAURICIO; LOURENCO, FERNANDO. Residues for flags of holomorphic foliations. ADVANCES IN MATHEMATICS, v. 320, p. 1158-1184, NOV 7 2017. (15/20841-5, 15/06697-9)

BRASSELET, JEAN-PAUL; MIWA LIBARDI, ALICE KIMIE; RIZZIOLLI, ELIRIS CRISTINA; SAIA, MARCELO JOSE. Cobordism of maps of locally orientable Witt spaces. PUBLICATIONES MATHEMATICAE-DEBRECEN, v. 94, n. 3-4, p. 299-317, 2019. (14/00304-2, 16/24707-4, 15/06697-9)