Timeline for Leray-Hirsch for HOMOLOGY?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Aug 31, 2016 at 21:39 | comment | added | Hari Rau-Murthy | Is that isomorphism true or is just true up to group extension? | |
| Nov 5, 2010 at 22:30 | comment | added | algori | A version of the Leray-Hirsch for homology is as follows: let $p:E\to B$ be a Serre fibration with $B$ connected and let $A$ be an abelian group. Assume that $p_\ast :H_\ast(F,A)\to H_\ast(E,A)$ is injective where $F$ is the fiber over some point of $B$, then $H_n(E,A)\cong \bigoplus_{i+j=n} H_i(B,H_j(F,A))$. The free module part is a bit tricky since, although the cohomology with coefficients in $A$ is always an $A$-algebra as long as $A$ is a commutative ring, the homology is not necessarily an $A$-coalgebra. | |
| Nov 5, 2010 at 21:43 | comment | added | Guangbo Xu | Sorry. I was stupid to miss this condition. | |
| Nov 5, 2010 at 21:42 | history | edited | Guangbo Xu | CC BY-SA 2.5 |
added 4 characters in body; added 43 characters in body; added 1 characters in body
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| Nov 5, 2010 at 21:17 | comment | added | Ben Webster♦ | It's automatic that the cohomology of E is a module over the cohomology of B. The point of Leray-Hirsch is that it is sometimes free. | |
| Nov 5, 2010 at 21:09 | history | asked | Guangbo Xu | CC BY-SA 2.5 |