HOMEWORK 10
(1) Using the long exact sequence of fibration, describe πk(RPn
) by πk(Sn
).
(2) Compute the fundamental group of double torus.
(3) Let X be a Klein bottle with two holes. Compute its fundamental group
(4) Using the Seifert–Van Kampen theorem compute the fundamental group of
R3
\ S1
.
Date: April 26, 2013.
1