Open strings in the cotangent bundle and Morse homotopy
Massachusetts Institute of Technology. Dept. of Mathematics.
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Let M be a riemannian manifold of dimension 3. We study the genus zero open rigid J-holomorphic curves in T*M with boundaries mapped in perturbations of the zero section. The perturbations of the zero section is defined fixing a. set of functions on M. We consider the graphs of the differential of the functions rescaled by an [epsilon] >/= 0. For a generic choice of the functions, we prove that, for E small enough, there exists a one to one correspondence between the J holomorphic curves and the planar Morse graphs of the functions.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.Includes bibliographical references (p. 51).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.; Massachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology