# Who first computed the integral cohomology ring of a weighted projective space (WPS) ?

After Jun-Ichi Igusa' talk at ICM 1962, H.J. Tramer computed the ring structure of the integral cohomology of such a space ( not yet called WPS ). In 1971 M.F. Atiyah called it WPS and established a Riemann-Roch theorem for it . This means that, more than ten years before Tetsuro Kawasaki, H.J. Tramer determined H*(WPS, Z). My question is : How to find Tramer's computations ? Who knows anything about H.J. Tramer ? A.Al-Amrani.

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Lastly I got a copy of H.J. Tramer's Ph.D.Thesis on the cohomology ring of "pseudo-projective sapaces" (1965), i.e. weighted projective spaces WPS (as they are called since the seventies).The question was posed to him by J. Igusa who,in his study of Siegel modular forms, had to do with WPS(2,3,5,6).The computation of the multiplicative sructure of H*(WPS, Z) by Tramer is based on works by A. Borel, Conner and Floyd (Transformation groups ,classifiant space for a group , spectral sequences, ... ). As did T. Kawasaky nearly ten years after him, he reduced the calculation to the case of what we call now "weighted lens space",denoted K^n (d) in his thesis. H.J. Tramer showed that for spaces of the same homotopy type as WPS, all "primary cohomological operations" (Steenrod squares,Pontrjagin squares, ...) are determined by the cup-product in H*(WPS,Z). He discussed also the question whether two WPS's are homotopic or not if their H*(.,Z)'s are isomorphic .

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I found myself the reference for H. J. Tramer's computation of the ring H*(WPS, Z) (WPS = weighted projective space) ! : "The cohomology ring of PSEUDO-PROJECTIVE SPACES" By TRAMER, Henry John. Ph. D. Thesis , Johns Hopkins University, 1965. (A.Al-Amrani, at.algebraic-topology/ag.algebraic-geometry ).

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I found the reference but not H.J.Tramer's thesis itself. –  Al-Amrani May 22 '13 at 13:08
To get a copy from Johns Hopkins University, the library in my University (Strasbourg,France) has to pay 65 \$ ! –  Al-Amrani Jun 15 '13 at 7:40