HOMEWORK 6
Exercise 1. Let X be the following space: Take the edges of tetrahedron with vertices
v0, v1, v2, v3 and add the centre p of the tetrahedron together with all the triangles
[vi, vj, p], 0 ≤ i < j ≤ 3.
Compute the local homology groups of X with respect to the point p, i.e. compute
H∗(X, X − {p}).
Exercise 2. Prove that the space which arises by gluing M¨obius band into a hole of
the sphere is the projective plane. Compute its homology and cohomology with Z/2
and Z/5 coefficients.
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