Chennai Mathematical Institute


MSc Thesis Seminar
2.00 pm, Seminar Hall
Construction of symplectic cobordisms

Yash Deshmukh
Chennai Mathematical Institute.


Construction of a symplectic structure on an almost symplectic manifold is a central problem in symplectic topology. This is closely related to the corresponding question for cobordisms. We introduce these questions, starting with necessary background from symplectic and contact topology. We then discuss the construction of symplectic structure on cobordisms which have handle-decomposition consisting of handles with index no more than half of the dimension. The main ideas of this construction are due to Eliashberg. Finally we describe a recent result of Eliashberg and Murphy which allows construction of symplectic structure even in presence of handles of higher indices, provided the concave end of the almost symplectic cobordism is overtwisted. If time permits, we give an outline of the proof.