Thesis (Ph. D.)--University of Rochester. Dept. of Mathematics, 2013.
This thesis consists of two parts. The fi rst part concentrates on polyhedral products.
Certain homotopy theoretic properties of polyhedral products, such as the
fundamental group, are investigated, and the results are used to compute certain
monodromy representations. Partial topological characterizations of transitively
commutative groups are also obtained using polyhedral products. The second part
concentrates on the spaces of commuting n-tuples in compact and connected Lie
groups. A new space is introduced, called X(2;G). The homology of the space
X(2;G) is computed with integer coffecients with the order of the Weyl group
inverted, and connections with classical representation theory are explored.
