We study connective Im(J)–theory for the classifying space Bℤ∕pa of a finite cyclic p–group and compute the Im(J)–cohomology groups completely. We also compute the Im(J)–homology groups, with the exception of a finite range of dimensions.
Knapp, Karlheinz  1
@article{10_2140_agt_2007_7_797,
author = {Knapp, Karlheinz},
title = {Connective {Im(J){\textendash}theory} for cyclic groups},
journal = {Algebraic and Geometric Topology},
pages = {797--828},
year = {2007},
volume = {7},
number = {2},
doi = {10.2140/agt.2007.7.797},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2007.7.797/}
}
Knapp, Karlheinz. Connective Im(J)–theory for cyclic groups. Algebraic and Geometric Topology, Tome 7 (2007) no. 2, pp. 797-828. doi: 10.2140/agt.2007.7.797
[1] , Lectures on generalised cohomology, from: "Category Theory, Homology Theory and their Applications, III (Battelle Institute Conference, Seattle, Wash., 1968, Vol. Three)", Springer (1969) 1
[2] , Stable homotopy and generalised homology, University of Chicago Press (1974)
[3] , The localization of spectra with respect to homology, Topology 18 (1979) 257
[4] , On the homotopy theory of $K$–local spectra at an odd prime, Amer. J. Math. 107 (1985) 895
[5] , , Applications of nonconnective $\mathrm{Im}(J)$–theory, from: "Handbook of algebraic topology", North-Holland (1995) 463
[6] , Commutative algebra, Graduate Texts in Mathematics 150, Springer (1995)
[7] , A note on some periodicity of $\mathrm{Ad}$–cohomology groups of lens spaces, Osaka J. Math. 23 (1986) 307
[8] , Splitting of $K$–theory and $g_{*}$ characteristic numbers, from: "Studies in algebraic topology", Adv. in Math. Suppl. Stud. 5, Academic Press (1979) 189
[9] , Stabil sphärische Elemente in der Bild-$J$–Homologie des klassifizierenden Raumes der zyklischen Gruppe mit $p$ Elementen, PhD thesis, Wuppertal (1992)
[10] , Connective $Im(J)$–theory for torsion-free spaces, the complex projective space as an example, preprint
[11] , On the $K$–homology of classifying spaces, Math. Ann. 233 (1978) 103
[12] , Stably spherical classes in the $K$–homology of a finite group, Comment. Math. Helv. 63 (1988) 414
[13] , Introduction to nonconnective $\mathrm{Im}(J)$–theory, from: "Handbook of algebraic topology", North-Holland (1995) 425
[14] , Anderson duality in $K$–theory and $\mathrm{Im}(J)$–theory, $K$–Theory 18 (1999) 137
[15] , , , Note on $J$–groups of lens spaces, Hiroshima Math. J. 7 (1977) 387
[16] , Diplomarbeit, Wuppertal
[17] , Zur $A$–Theorie von $B\mathbb{Z}/p^{2}$, Diplomarbeit, Wuppertal (1992)
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