List of Fundamental Groups for 2-Manifolds

Theorem
For the following two-manifolds, the fundamental group for any point in $X$, written $\map {\pi_1} X$ is isomorphic to the listed group:


 * $\map {\pi_1} {\Bbb S^1 \times \closedint 0 1} = \Z$


 * $\map {\pi_1} {\Bbb S^2} = \set e$, the trivial group.


 * $\map {\pi_1} {\Bbb T^2} = \map {\pi_1} {\Bbb S^1 \times \Bbb S^1} = \Z \times \Z$


 * $\map {\pi_1} {\Bbb {RP}^2} = \Z_2$