Timeline for Calculation of Restriction Map
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Jul 10, 2015 at 19:19 | comment | added | Steve Costenoble | I don't think I've seen it written out (or done so myself), and it's been a while since I thought about it, but I think it goes like this: If you view Bredon cohomology as Mackey-functor valued, then there's a Kunneth spectral sequence whose $E_2$ term involves Tor groups taken in the category of Mackey functors, i.e., derived functors of the box product. It converges to the cohomology of the product, with appropriate finiteness conditions to get convergence. | |
| Jul 7, 2015 at 3:58 | comment | added | Surojit Ghosh | @SteveCostenoble : Is there any internal Kunneth formula for integer graded Bredon cohomology theory , i.e. We know the integer graded Bredon cohomology of $G$-spaces $X ,Y$ respectively and we wanted to know about the Bredon cohomology of $X \times Y$ ? | |
| Apr 5, 2015 at 16:06 | comment | added | Steve Costenoble | Sorry: I've told you how I would go about it, but I have too many other projects of my own at the moment to spend time on the actual calculation. | |
| Apr 4, 2015 at 11:36 | comment | added | Surojit Ghosh | @SteveCostenoble : I know the explicit $Z/6$-CW($\xi^2$)-complex structure of $D(\xi^2)$ . I am looking for an explicit calculation for $Z/6$-CW($\xi^2$)-complex structure of $D(2\xi^2)$ .it'll be great if you kindly calculate the explicit (geometric) structure of it. | |
| Mar 31, 2015 at 20:19 | comment | added | Steve Costenoble | As I said, I tend to think of $S(V+W) = \partial D(V+W) = \partial [D(V)\times D(W)]$. The chain complex of $D(V)\times D(W)$ wants to look like the tensor product of the two chain complexes, except for one wrinkle: a product of ${\mathbb Z}/6$ cells is not a single cell, but a disjoint union of several. If you view the chains as Mackey functors and use the box product, this should be taken into account correctly. That may or may not give you a good handle on the geometry, but that's how I would approach the algebra. | |
| Mar 31, 2015 at 0:57 | comment | added | Surojit Ghosh | @SteveCostenoble:We know that $S(V+W)= S(V)*S(W)$.Now I know the $Z/6$ CW complex structures of $S(\xi^2)$ and $S(2\sigma)$.How can I compute the attaching maps for $S(\xi^2 + 2\sigma)$? | |
| Mar 23, 2015 at 19:35 | comment | added | Surojit Ghosh | @SteveCostenoble: Thank you very much.You are such an inspiration for me. | |
| Mar 23, 2015 at 15:55 | comment | added | Steve Costenoble | I must be misremembering, as I can't find any calculations now for groups other than ${\mathbb Z}/p$. I don't know the structure on $S(\xi+\xi^2+2\sigma)$ offhand, but if I wanted to work it out I would first put structures on $D(\xi)$, $D(\xi^2)$, and $D(2\sigma)$, then take their product and look at what the structure on the boundary is. | |
| Mar 22, 2015 at 1:23 | comment | added | Surojit Ghosh | @SteveCostenoble : Thank you for your valuable comment.I had read most of the papers of Gaunce Lewis and Jeff Caruso(just One paper).But I never saw any paper on the calculation $H^*_{G}(*,M)$ for $|G| = p^n$.It will be nice if you can find it for me.I have another question that'll help me for the above calculation.Question:What is $Z/6$-complex structure of $S(\xi + \xi^2 + 2\sigma)$ ? Where $\xi$ ,$\xi^2$ are defined in above comment and $\sigma$ is 1 real dimensional sign representation of $Z/6$. | |
| Mar 20, 2015 at 16:59 | comment | added | Steve Costenoble | Unfortunately, the only computations I know of are for $G = {\mathbb Z}/p$ for $p$ prime. (Look for papers by L. Gaunce Lewis, Jeff Caruso, and William Kronholm.) I think I saw a paper also looking at prime power order, but can't seem to find it. | |
| Mar 20, 2015 at 13:37 | comment | added | Surojit Ghosh | @SteveCostenoble: Thank you very much for your comment.I am interested in $ G = Z/6 $, $ M = Z/6$-constant Mackey functor and $\alpha = \xi^2 - \xi$, where $\xi$- is nontrivial irreducible representation of $Z/6$ with out fixed point.Is it possible to find $i^*$ in this setting? | |
| Mar 19, 2015 at 19:15 | comment | added | Steve Costenoble | I don't think we even know $H_G^*(*;M)$ for all finite abelian groups, in $RO(G)$ grading. However, the calculations I've seen are Mackey-functor valued, so include all the restriction maps and transfers. | |
| Mar 19, 2015 at 16:51 | history | edited | Surojit Ghosh | CC BY-SA 3.0 |
improved formatting
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| Mar 18, 2015 at 0:13 | history | asked | Surojit Ghosh | CC BY-SA 3.0 |