It's topology 2; the syllabus would approximately be:
homotopy groups (homotopy groups of spheres, relative homotopy groups and the long exact sequence of a pair, hopf fibration and the long exact sequence of a fibration), then singular homology (excision, jordan-brouwer splitting theorem), CW complexes (hurewicz, whitehead), homology with coefficients, cohomology (cellular/singular, künneth's formula), poincare duality and then some