Homological finiteness properties

• Grant number: 15/22064-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: March 01, 2016
• End date: February 29, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Dessislava Hristova Kochloukova
• Grantee: Luis Augusto de Mendonça
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated scholarship(s): 16/24778-9 - Homological finiteness properties of Lie algebras, BE.EP.DR

Abstract

The first topic of the project is to study the Sigma theory of wreath products and of the class of groups defined in P. H. Kropholler, A. Martino, arXiv:1407.0302. Some partial results on the Sigma theory of wreath product were already obtained inBartholdi, de Cornulier, Kochloukova, Q. J. Math. 66 (2015), no. 2, 437 - 457.During his master thesis the student studied the paper of Bartholdi, de Cornulier, Kochloukova.The second topic of research is to generalize a construction of a group (related to weak commutativity) defined in Sidki, J. Algebra 63 (1980), no. 1, 186 - 225and its generalization suggested in Lima, PhD thesis, UnB, 2014. We believe that the new methods suggested in Kochloukova, Sidki, On weak commutativity of groups, submited, will be usefull to conclude this project. Finally, since the generalization of the Sidki group has as a quotient some wreath product there is a link between both projects i.e. results from the first project can be useful in the solution of the second.

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)

KOCHLOUKOVA, DESSISLAVA H.; MENDONCA, LUIS. Weak commutativity for pro-pgroups. MONATSHEFTE FUR MATHEMATIK, v. 194, n. 3, p. 555-575, MAR 2021. (15/22064-6, 18/23690-6)

DE MENDONCA, LUIS AUGUSTO. ON THE Sigma-INVARIANTS OF WREATH PRODUCTS. PACIFIC JOURNAL OF MATHEMATICS, v. 298, n. 1, p. 113-139, JAN 2019. (16/24778-9, 15/22064-6)

DE MENDONCA, LUIS AUGUSTO. The weak commutativity construction for Lie algebras. Journal of Algebra, v. 529, p. 145-173, JUL 1 2019. (16/24778-9, 15/22064-6)

DE MENDONCA, LUIS AUGUSTO. Weak commutativity and nilpotency. Journal of Algebra, v. 564, p. 24-pg., 2020-12-15. (15/22064-6)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MENDONÇA, Luis Augusto de. Propriedades homológicas de finitude. 2020. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.