Applications of algebraic topology to configuration spaces

Abstract

In this thesis, our focus is on the configuration space F(M, k) of a manifold Mto be defined below. We study some basic properties of the configuration spacesuch as the homotopy groups, homology and cohomology structure. We describea certain nontrivial presentation of the fundamental group of F(R2, k). We alsodiscuss the cohomology structure of the configuration space F(M, k) where M is aRiemann surface without boundary and projective spaces FP2 (Here F = R,C).