dc.contributor.author Jia, Bei en dc.date.accessioned 2014-03-14T20:34:36Z en dc.date.available 2014-03-14T20:34:36Z en dc.date.issued 2013-04-19 en dc.identifier.other etd-04292013-182032 en dc.identifier.uri http://hdl.handle.net/10919/32039 en dc.description.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. en dc.publisher Virginia Tech en dc.relation.haspart Jia_B_T_2013_R1.pdf en dc.rights In Copyright en dc.rights.uri http://rightsstatements.org/vocab/InC/1.0/ en dc.subject D-brane en dc.subject K-theory en dc.subject K-homology en dc.subject String theory en dc.title D-branes and K-homology en dc.type Thesis en dc.contributor.department Mathematics en dc.description.degree Master of Science en thesis.degree.name Master of Science en thesis.degree.level masters en thesis.degree.grantor Virginia Polytechnic Institute and State University en thesis.degree.discipline Mathematics en dc.contributor.committeechair Haskell, Peter E. en dc.contributor.committeemember Floyd, William J. en dc.contributor.committeemember Linnell, Peter A. en dc.contributor.committeemember Sharpe, Eric R. en dc.identifier.sourceurl http://scholar.lib.vt.edu/theses/available/etd-04292013-182032/ en dc.date.sdate 2013-04-29 en dc.date.rdate 2013-06-03 en dc.date.adate 2013-06-03 en
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