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Topic:
Top Homology of Manifold with Boundary is Zero. True? Why?
Replies:
2
Last Post:
May 28, 2013 11:54 PM



Bacle H
Posts:
283
Registered:
4/8/12


Top Homology of Manifold with Boundary is Zero. True? Why?
Posted:
May 14, 2013 7:36 PM


Hi, All:
I'm trying to see if it is true that the top homology of
an nmanifold with boundary is zero. I have tried some examples;
a closed annulus ( homotopic to S^1 , so H^2(S^1)=0 , R^n with
a boundary copy of some R^m m<n retracts to R^m , etc.)
It seems strange that a manifold would "lose its orientability"
if we cappedin a boundary. It seems like this boundary would bound
all the ncycles that had no boundary before the boundary was cappedin;
otherwise, how is the quotient Cycles/Boundaries suddenly zero?
I tried some MAyerVietoris, but got nowhere. Any Ideas?
Thanks.



