{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/32039"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/32039","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"D-branes and K-homology","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.","abstract_html":"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<span class=\"etd-inline-math\"><sup>c</sup></span> 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.","abstract_has_math":true,"creators":["Jia, Bei"],"institution":"Virginia Tech","degree_name":"Master of Science","degree_level":"masters","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Haskell, Peter E."],"committee_members":["Floyd, William J.","Linnell, Peter A.","Sharpe, Eric R."],"year":2013,"date_issued":"2013-04-19","date_published":"2013-04-19","updated_at":"2026-07-22T22:20:00Z","subjects":["D-brane","K-theory","K-homology","String theory"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-04292013-182032"],"render_values":[{"text":"etd-04292013-182032","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/32039","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Haskell, Peter E."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Floyd, William J.","Linnell, Peter A.","Sharpe, Eric R."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Jia, Bei"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:34:36Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:34:36Z","2013-06-03"]},{"key":"dc:date.issued","label":"Date","values":["2013-04-19"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["D-brane","K-theory","K-homology","String theory"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-04292013-182032"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/32039"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science"]},{"key":"dc:title","label":"Title","values":["D-branes and K-homology"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Haskell, Peter E."],"dc:contributor.committeemember":["Floyd, William J.","Linnell, Peter A.","Sharpe, Eric R."],"dc:contributor.department":["Mathematics"],"dc:creator":["Jia, Bei"],"dc:date.accessioned":["2014-03-14T20:34:36Z"],"dc:date.available":["2014-03-14T20:34:36Z","2013-06-03"],"dc:date.issued":["2013-04-19"],"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."],"dc:description.degree":["Master of Science"],"dc:identifier.other":["etd-04292013-182032"],"dc:identifier.uri":["http://hdl.handle.net/10919/32039"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["D-brane","K-theory","K-homology","String theory"],"dc:title":["D-branes and K-homology"],"dc:type":["Thesis"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["masters"],"thesis:degree_name":["Master of Science"],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:00Z"}