Introduction to Contact Geometry by Dheeraj Kulkarni

Explore the foundations of contact geometry in this comprehensive lecture from the International Centre for Theoretical Sciences. Delve into key concepts such as the Frobenius theorem, local theory of contact manifolds, contactomorphisms, and the Gray stability theorem. Examine the relationship between contact and symplectic structures, and learn about contact submanifolds of symplectic manifolds. Gain insights into J-holomorphic curves, Gromov-Witten invariants, and their connections to complex algebraic geometry and physics. Progress from introductory material to advanced topics, including lemmas and proofs, to develop a thorough understanding of this important area of mathematics.

J-Holomorphic Curves and Gromov-Witten Invariants
Introduction to Contact Geometry
Goal
Contact Geometry
References
Frobenius theorem
Remark
Example
Contract structure
Local theory of contact manifolds
Contactomorphism
Gray stability theorem
Simplistic structure
Simplistic Geometry
Lemma 1
Proof
Lemma 2
Contact submanifolds of symplectic manifold
Recall
Symplectization of a contact form