Hatcher-Algebraic-Topology · Problem 33

Cohomology

Mathematics — Graph Theory · contractible-manifold-boundary-homology-sphere

Problem

Show that if

M

is a compact contractible

n

-manifold then

\partial M

is a homology

(n-1)

-sphere, that is,

H_i(\partial M;\mathbb{Z})\approx H_i(S^{n-1};\mathbb{Z})

for all

i