Abstract
In this thesis the close relationship between the topological $K$homology group of the spacetime manifold $X$ of string theory and Dbranes in string theory is examined. An element of the $K$homology group is given by an equivalence class of $K$cycles $[M,E,\phi]$, where $M$ is a closed spin$^c$ manifold, $E$ is a complex vector bundle over $M$, and $\phi: M\rightarrow X$ is a continuous map. It is proposed that a $K$cycle $[M,E,\phi]$ represents a Dbrane configuration wrapping the subspace $\phi(M)$. As a consequence, the $K$homology element defined by $[M,E,\phi]$ represents a class of Dbrane configurations that have the same physical charge. Furthermore, the $K$cycle representation of Dbranes resembles the modern way of characterizing fundamental strings, in which the strings are represented as twodimensional surfaces with maps into the spacetime manifold. This classification of Dbranes also suggests the possibility of physically interpreting Dbranes wrapping singular subspaces of spacetime, enlarging the known types of singularities that string theory can cope with.
