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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Geometric Interpretation of (lower) Cohomology?

**Physics Forums | Science Articles, Homework Help, Discussion**