### Title page for ETD etd-04292013-182032

Type of Document Master's Thesis
Author Jia, Bei
URN etd-04292013-182032
Title D-branes and K-homology
Degree Master of Science
Department Mathematics
Eric R. Sharpe Committee Member
Peter A. Linnell Committee Member
William J. Floyd Committee Member
Keywords
• D-brane
• K-theory
• K-homology
• String theory
Date of Defense 2013-04-19
Availability unrestricted
Abstract
In this thesis the close relationship between the topological $K$-homology group of the spacetime manifold $X$ of string theory and D-branes 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 D-brane configuration wrapping the subspace $\phi(M)$. As a consequence, the $K$-homology element defined by $[M,E,\phi]$ represents a class of D-brane configurations that have the same physical charge. Furthermore, the $K$-cycle representation of D-branes resembles the modern way of characterizing fundamental strings, in which the strings are represented as two-dimensional surfaces with maps into the spacetime manifold. This classification of D-branes also suggests the possibility of physically interpreting D-branes wrapping singular subspaces of spacetime, enlarging the known types of singularities that string theory can cope with.
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