Geodesic
On BP<1>*(K(Z, 3); Z/p)
Canadian journal of mathematics, Tome 35 (1983) no. 4, pp. 630-653

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we study the inverse limit cohomology h*(K(Z, 3)) of an Eilenberg-MacLane object K(Z, 3) for certain cohomology theories h. Our main result gives a complete description of all non-trivial differentials of the Atiyah-Hirzebruch spectral sequence (AHSS) H*(X;h*(pt)) ⇒ h*(X) for X = K(Z, 3) and h either of the complex K-theories K*( ;Z/p) and K*( ;Z(p) ). This is achieved inductively using the finite symmetric product spaces SPkS 3, k = pr. Identification of cycles and boundaries of each non-trivial differential leads to an explicit description of BP<1>*(K(Z, 3); Z/p) and some information about BP<1>*(K(Z, 3)). 
Ucci, Jack. On BP<1>*(K(Z, 3); Z/p). Canadian journal of mathematics, Tome 35 (1983) no. 4, pp. 630-653. doi: 10.4153/CJM-1983-036-3
@article{10_4153_CJM_1983_036_3,
     author = {Ucci, Jack},
     title = {On {BP&lt;1&gt;*(K(Z,} 3); {Z/p)}},
     journal = {Canadian journal of mathematics},
     pages = {630--653},
     year = {1983},
     volume = {35},
     number = {4},
     doi = {10.4153/CJM-1983-036-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-036-3/}
}
TY  - JOUR
AU  - Ucci, Jack
TI  - On BP<1>*(K(Z, 3); Z/p)
JO  - Canadian journal of mathematics
PY  - 1983
SP  - 630
EP  - 653
VL  - 35
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-036-3/
DO  - 10.4153/CJM-1983-036-3
ID  - 10_4153_CJM_1983_036_3
ER  - 
%0 Journal Article
%A Ucci, Jack
%T On BP<1>*(K(Z, 3); Z/p)
%J Canadian journal of mathematics
%D 1983
%P 630-653
%V 35
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-036-3/
%R 10.4153/CJM-1983-036-3
%F 10_4153_CJM_1983_036_3

[1] 1. Anderson, D. W., Universal coefficient theorems for K-theory (preprint). Google Scholar

[2] 2. Anderson, D. W. and Hodgkin, L., The K-theory of Eilenberg-MacLane complexes. Topology 7(1968), 317–380. Google Scholar

[3] 3. Araki, S. and Toda, H., Multiplicative structures in mod q cohomology theories I, Osaka J. Math. 2 (1965), 71–115. Google Scholar

[4] 4. Atiyah, M. F. and Hirzebruch, F., Analytic cycles on complex manifolds, Topology 7 (1961), 24–45. Google Scholar

[5] 5. Cartan, H., Exposés 9, 10, 11 of Algehres d'Eilenberg-MacLane et homotopie, Séminaire Henri Cartan (1954/1955). Google Scholar

[6] 6. Dold, A. and Thorn, R., Quasifaserungen and unendliche symmetrische Produkte, Ann. of Math. 67 (1958), 239–281. Google Scholar

[7] 7. Hodgkin, L., On the K-theory of Lie groups, Topology 6 (1967), 1–36. Google Scholar

[8] 8. Johnson, D. C. and Wilson, W. Stephen, Projective dimension and Brown-Peterson homology, Topology 12 (1973), 327–353. Google Scholar

[9] 9. Kultze, R., Über multiplikative Eigenschaften von spektralen Sequenzen, Math. Annalen 158 (1965), 233–268. Google Scholar

[10] 10. Nakaoka, M., Cohomology mod p of symmetric products of spheres 11, J. Inst. Polyteeh., Osaka City Univ. 10 (1959), 67–89. Google Scholar

[11] 11. Serre, J.-P., Cohomologie modulo 2 des complexes d'Eilenberg-MacLane, Comm. Math. Helv. 27 (1953), 198–231. Google Scholar

[12] 12. Snaith, V. and Ucci, J. J., Three remarks on symmetric products and symmetric maps, Pac. J. Math. 45, 369–377. Google Scholar

Cité par Sources :