Geometric topology of continuous function algebras

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Functional analytic study of dynamical system on compact metric was the central theme of the research based on the research grant. The focus is on theweighted composition operators on continuous function algebras. Associated with each dynamical system, an abelian group of unimodular weight for which the operators have eigenvalues was defined and it turned out the group carries both topological and measure theoretic aspects of the system. The result was generalized to group-action dynamics and an abelian group of 1-cocycle with similar property was defined and studied.