Hi, All:(adsbygoogle = window.adsbygoogle || []).push({});

Just curious to know if there is an interpretation for lower cohomology that is as

"nice", as that of the lower fundamental groups, i.e., Pi_0(X) =0 if X is path-connected

(continuous maps from S^0:={-1,1} into a space X are constant), and Pi_1(X)=0 if

X is path-connected + simply-connected. Are there similarly-nice interpretations

for Cohomology groups, i.e., what can we know about a space X if we

know that H^0(X)=0 , and/or if H_1(X)=0 ? I am aware of Hurewicz' Theorem

(hip, hip Hurewicz) , and of Poincare Duality, but Ii don't see how to get a nice

geometric picture from this. Any Ideas/Suggestions?

Thanks.

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# Geometric Interpretation of (lower) Cohomology?

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