The connective K-theory of elementary abelian p-groups for odd primes

For an odd prime p, we aim to do some calculations of connective K-theory of elementary abelian groups V(r), where V(r) denotes an elementary abelian p-group of rank r. The methods involve a combination of Adams spectral sequence (ASS) calculations together with local cohomology calculations. The overall plan builds on and takes its inspiration from work of J. Greenlees and R. Bruner. As a step towards the Gromov-Lawson-Rosenberg (GLR) conjecture for V(r), the thesis calculates the complex connective K-cohomology, ku^*(BV(r)), for r ≤ 3, and the complex connective K-homology, ku_*(BV (r)) for p = 3 and r ≤ 2.