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Igor Sikora
Igor Sikora
10:17 AM
Hi all, I've got a problem with understanding Mike Hill's work on D(\sigma)-algebras (my yesterday's question was also indirectly refering to this paper)
Going to the problem:
He is claiming that if X is a space s.th. its homology is free over a ring R on some graded set S, then the Bredon homology of Map_e(C_2,X) is free on the graded set Map_e(C_2,S)
With a special grading given by deg(f)=deg(f(e))+deg(f(g)) if f(e)\neq f(g)
(Bredon homology w/coeff's in N_e^{C_2}R, that's important point)
and deg(f)=deg(f(e))\rho if f(e)=f(g)
So do I understand correctly that this implies Bredon homology of a point being concentrated in degree 0?
RO(C_2) graded homology
 
 
9 hours later…
Saal Hardali
Saal Hardali
7:37 PM
In the following paper by Davis and Mahowald (https://www.jstor.org/stable/2000922) there's the following remark at the end of the introduction:

"While this paper was being refereed, David Eisen, in his Ph.D. thesis, generalized our results... and simplified the proof"

I tried googling around for this thesis but couldn't seem to find it. Does anyone have (and/or knows where and how to get) access to this document?
 
 
2 hours later…
Andrew Senger
Andrew Senger
9:15 PM
 
Dylan Wilson
Dylan Wilson
@IgorSikora here 'free' means 'a direct sum of RO(C_2)-graded shifts of N(R)', so the actual homotopy groups will be free as an RO(C_2)-graded module over N(R)_{fancy star} (which is not concentrated in degree 0)
(sorry, I guess both those 'N(R)'s should be 'HN(R)'s to make it less confusing)
 

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