1Assistant Professor, Department of Mathematics, Srimed Andavan Arts & Science College, Trichy, Tamil Nadu, 620005, India, E-mail: andavanmathsramesh@gmail.com
2Assistant Professor, Department of Mathematics, M.I.E.T Engineering College, Trichy, Tamil Nadu, 620007, India E-mail: prabhu.rajamanikam@gmail.com
*Corresponding Author: A. Rameshkumar, Assistant Professor & Research Adviser, Department of Mathematics, Srimad Andavan Arts and Science College (Autonomous) No.7, Nelson Road, T.V. Kovil, Trichy, Tamil Nadu, 620005, India E-mail: andavanmathsramesh@gmail.com
2010 Mathematics Subject Classification: 12Jxx
We determine the category of boundary conditions in the case that the closed string algebra is semisimple. We find that sewing constraints-the most primitive form of worldsheet locality-already imply that Dbranes are vector bundles on spacetime. This expository paper describes sewing conditions in twodimensional open and closed topological field theory. We include a description of the G-equivariant case, where G is a finite group. We comment on extensions to cochain-valued theories and various applications.
D-branes, Topological field theory, Cochain level theory
