Title page for ETD etd-04292013-182032

Type of Document Master's Thesis
Author Jia, Bei
Author's Email Address
URN etd-04292013-182032
Title D-branes and K-homology
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Peter E. Haskell Committee Chair
Eric R. Sharpe Committee Member
Peter A. Linnell Committee Member
William J. Floyd Committee Member
  • D-brane
  • K-theory
  • K-homology
  • String theory
Date of Defense 2013-04-19
Availability unrestricted
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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