Semigroups of Mappings: Set Theoretic, Analytic, and Combinatorial Aspects

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The aim of this project is to investigate the connections between relative ranks of various natural semigroups and certain small cardinal invariants, such as those in Cichon's diagram. The relative rank of a subsemigroup T of a semigroup S is the least cardinal of a subset of S that together with T generates the whole of S. As such, relative ranks can be seen as an infinite analogue of the classical notion of rank, i.e. the least number of generators. The investigators propose to perform this research in collaboration with Professors Cichon and Morayne (Wroclaw University of Technology, Poland). Support is sought for travel and subsistence for the principal investigator to make four visits to Poland, to carry out collaborative research. The proposed project combines aspects of topology, algebra, combinatorics, and set theory. The combined expertise of the investigator and Professors Cichon and Morayne encompasses these fields of research.