# cohomology of a closed surface

Let Σ2 be a closed oriented surface of genus 2. Compute H∗(Σ2, A; Z) where (i) A is a separating simple closed curve [which cuts Σ2 into two genus one pieces with one boundary component each] (ii) A is a non-separating simple closed curve [cutting along which gives a genus one surface with two holes] and (iii) A is a simple closed curve which bounds an embedded disc in Σ2.