We aim to discuss the primary result of the paper "A new construction of symplectic manifolds" by Robert E. Gompf, which asserts that there are many more symplectic manifolds compared to Kähler manifolds. In today's talk, we will begin with the very basics of symplectic geometry, and in the following few discussions, we will consider the key construction.
Symplectic linear algebra, Symplectic form and cup product
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