UC Berkeley

Homological mirror symmetry (HMS) asserts that the Fukaya category of a symplectic manifold

is derived equivalent to the category of coherent sheaves on the mirror complex manifold.

Without suitable enlargement (split closure) of the Fukaya category, certain objects of it are

missing to prevent HMS from being true. One possible solution is to include coisotropic

branes into the Fukaya category. This thesis gives a construction for linear symplectic tori of

a version of Fukaya category including coisotropic branes by using a doubling procedure, and

discussing the relation between the Fukaya category of the doubling torus and the Fukaya

category of the original torus.