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Results tagged with homology
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user 4760
Homology is a general way of associating a sequence of algebraic objects such as abelian groups or modules to other mathematical objects such as topological spaces.
16
votes
1
answer
5k
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Is it true that all real projective space $RP^n$ can not be smoothly embedded in $R^{n+1}$ f...
$RP^3$ can not be embedded proving by homology thoery (Alexander sphere duality, lefschetz duality and a long exact sequence).
For the other cases, I do not know how to prove. …
- 1,598
9
votes
Why torsion is important in (co)homology ?
Integer Pontrjagin classes are diffeomorphism invariant, while rational Pontrjagin classes are homeomorphism invariant, due to Novikov. Also there are examples where two smooth manifolds are homeomor …