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dc.contributor.authorJia, Beien
dc.date.accessioned2014-03-14T20:34:36Zen
dc.date.available2014-03-14T20:34:36Zen
dc.date.issued2013-04-19en
dc.identifier.otheretd-04292013-182032en
dc.identifier.urihttp://hdl.handle.net/10919/32039en
dc.description.abstractIn 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.publisherVirginia Techen
dc.relation.haspartJia_B_T_2013_R1.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectD-braneen
dc.subjectK-theoryen
dc.subjectK-homologyen
dc.subjectString theoryen
dc.titleD-branes and K-homologyen
dc.typeThesisen
dc.contributor.departmentMathematicsen
dc.description.degreeMaster of Scienceen
thesis.degree.nameMaster of Scienceen
thesis.degree.levelmastersen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.disciplineMathematicsen
dc.contributor.committeechairHaskell, Peter E.en
dc.contributor.committeememberFloyd, William J.en
dc.contributor.committeememberLinnell, Peter A.en
dc.contributor.committeememberSharpe, Eric R.en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-04292013-182032/en
dc.date.sdate2013-04-29en
dc.date.rdate2013-06-03en
dc.date.adate2013-06-03en


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