Timeline for Pontryagin Product on the Homology of $CP^{\infty}$
Current License: CC BY-SA 3.0
3 events
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| Apr 14, 2013 at 10:30 | comment | added | Callan McGill | The Hopf algebra structure on homology is dual to cohomology. One often uses that the diagonal of a generator in cohomology is easy to work out (for degree reasons) and that it is an algebra map. The Hopf algebra structure on $H^{*}(CP^{\infty};R)$ is given by $R[[x]]$ where x is primitive and so the dual Hopf algebra structure on homology will be a divided power algebra where the element dual to $x$ is primitive (and this determines the rest of the structure). One can think of this as the algebra with generators $\frac{1}{k!}\frac{d^{k}}{dx^{k}}$ and the coproduct as given by the Leibniz rule | |
| Apr 14, 2013 at 10:01 | comment | added | Fernando Muro | Look it up in "Topology of Lie groups I, II" by Mimura and Toda. | |
| Apr 14, 2013 at 7:10 | history | asked | Xing Gu | CC BY-SA 3.0 |