1.II.21F

Algebraic Topology
Part II, 2008

(i) State the van Kampen theorem.

(ii) Calculate the fundamental group of the wedge S2S1S^{2} \vee S^{1}.

(iii) Let X=R3\AX=\mathbb{R}^{3} \backslash A where AA is a circle. Calculate the fundamental group of XX.