Universal topological groups

• Grant number: 12/20084-1
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: May 01, 2013
• End date: April 30, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valentin Raphael Henri Ferenczi
• Grantee: Brice Rodrigue Mbombo Dempowo
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The question of the existence of a universal topological group interested many mathematicians over the last few years. The question in the case of Polish groups was formulated by Ulam in 1935 and solved by Uspenskij in 1986. Other positive answers were given to the question of the existence of a universal Polish group, Uspenskij 1990, and Ben Yacoov 2012, the solution being the isometry group of some natural universal Polish space (Urysohn's space for Uspenskij, Gurarij' space for Ben Yacoov). The question of the existence of a topological group of uncountable weight remains open. The objective of this project is to study this question, looking for solutions among isometry groups of universal objects of uncountable weight; to find other natural examples or more natural proofs of previous results in the separable case; and study a few other related problems.

Scientific publications

(6)

(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)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. The Ramsey property for Banach spaces and Choquet simplices, and applications. COMPTES RENDUS MATHEMATIQUE, v. 355, n. 12, p. 1242-1246, DEC 2017. (12/20084-1, 13/24827-1, 13/14458-9)

FERENCZI, V; LOPEZ-ABAD, J.; MBOMBO, B.; TODORCEVIC, S.. Amalgamation and Ramsey properties of L-p spaces. ADVANCES IN MATHEMATICS, v. 369, p. 76-pg., 2020-08-05. (16/25574-8, 12/20084-1, 13/24827-1, 13/11390-4)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. THE RAMSEY PROPERTIES FOR GRASSMANNIANS OVER R, C. COMBINATORICA, NOV 2021. (12/20084-1, 13/24827-1, 13/14458-9)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. The Ramsey property for operator spaces and noncommutative Choquet simplices. JOURNAL OF FUNCTIONAL ANALYSIS, v. 281, n. 9, NOV 1 2021. (13/24827-1, 12/20084-1, 13/14458-9, 16/25574-8)

BARROSO, CLEON S.; MBOMBO, BRICE R.; PESTOV, VLADIMIR G.. On topological groups with an approximate fixed point property. Anais da Academia Brasileira de Ciências, v. 89, n. 1, p. 19-30, MAR 2017. (12/20084-1)

BARTOSOVA, DANA; LOPEZ-ABAD, JORDI; LUPINI, MARTINO; MBOMBO, BRICE. The Ramsey property for Banach spaces and Choquet simplices. JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, v. 24, n. 4, p. 36-pg., 2022-01-01. (12/20084-1, 13/24827-1, 13/14458-9)