The ER(z)-cohomology of BZ/(2q ) and CPn
Canadian journal of mathematics, Tome 70 (2018) no. 1, pp. 191-217

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

The $ER\left( 2 \right)$ -cohomology of $B\mathbb{Z}/\left( {{2}^{q}} \right)$ and $\mathbb{C}{{\mathbb{P}}^{n}}$ are computed along with the Atiyah–Hirzebruch spectral sequence for $ER{{\left( 2 \right)}^{*}}\left( \mathbb{C}{{\mathbb{P}}^{\infty }} \right)$ . This, along with other papers in this series, gives us the $ER\left( 2 \right)$ -cohomology of all Eilenberg–MacLane spaces.
DOI : 10.4153/CJM-2017-003-5
Mots-clés : 55N20, 55N91, 55P20, 55T25, complex projective space, cohomology theory, Eilenberg–MacLane space, Atiyah–Hirzebruch spectral sequence
Kitchloo, Nitu. The ER(z)-cohomology of BZ/(2q ) and CPn. Canadian journal of mathematics, Tome 70 (2018) no. 1, pp. 191-217. doi: 10.4153/CJM-2017-003-5
@article{10_4153_CJM_2017_003_5,
     author = {Kitchloo, Nitu},
     title = {The {ER(z)-cohomology} of {BZ/(2q} ) and {CPn}},
     journal = {Canadian journal of mathematics},
     pages = {191--217},
     year = {2018},
     volume = {70},
     number = {1},
     doi = {10.4153/CJM-2017-003-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-003-5/}
}
TY  - JOUR
AU  - Kitchloo, Nitu
TI  - The ER(z)-cohomology of BZ/(2q ) and CPn
JO  - Canadian journal of mathematics
PY  - 2018
SP  - 191
EP  - 217
VL  - 70
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-003-5/
DO  - 10.4153/CJM-2017-003-5
ID  - 10_4153_CJM_2017_003_5
ER  - 
%0 Journal Article
%A Kitchloo, Nitu
%T The ER(z)-cohomology of BZ/(2q ) and CPn
%J Canadian journal of mathematics
%D 2018
%P 191-217
%V 70
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-003-5/
%R 10.4153/CJM-2017-003-5
%F 10_4153_CJM_2017_003_5

[Ban13] [Ban13] Banerjee, R., On the ER(2)-cohomology of some odd-dimensional projective spaces. Topology Appl. 160(2013), 1395–1405. http://dx.doi.Org/10.1016/j.topol.2013.05.017 Google Scholar

[HK01] [HK01] Hu, P. and Kriz, I., Real-oriented homotopy theory and an analogue of the Adams-Novikov spectral sequence. Topology 40(2001), 317–399. Google Scholar | DOI

[HM16] [HM16] Hill, M. A. and Meier, L., The C-spectrum TMF and its invertible modules. arxiv:1 507.08115v3 Google Scholar

[JW73] [JW73] Johnson, D. C. and Wilson, W. S., Projective dimension and Brown-Peterson homology. Topology 12(1973), 327–353. Google Scholar | DOI

[KLW16] [KLW16] Kitchloo, N., Lorman, V., and Wilson, W. S., Landweber flat real pairs, and ER(n)-cohomology. 2016. arxiv:1 603.06865 Google Scholar

[KW07a] [KW07a] Kitchloo, N. and Wilson, W. S., On fibrations related to real spectra. In: Proceedings of the Nishida Fest (Kinosaki 2003), Geom. Topol. Monogr., 10, Geom. Topol. Publ., Coventry, 2007, pp. 237–244. Google Scholar | DOI

[KW07b] [KW07b] Kitchloo, N. and Wilson, W. S., On the Hopf ring for ER(n). Topology Appl. 154(2007), 1608–1640. Google Scholar | DOI

[KW08a] [KW08a] Kitchloo, N. and Wilson, W. S., The second real Johnson-Wilson theory and non-immersions of RPn. Homology Homotopy Appl. 10(2008), 223–268. Google Scholar | DOI

[KW08b] [KW08b] Kitchloo, N. and Wilson, W. S., The second real Johnson-Wilson theory and non-immersions of RPn. II. Homology Homotopy Appl. 10(2008), 269–290. Google Scholar | DOI

[KW13] [KW13] Kitchloo, N. and Wilson, W. S., Unstable splittings for real spectra. Algebr. Geom. Topol. 13(2013), 1053–1070. http://dx.doi.Org/10.214O/agt.2O13.13.1053 Google Scholar

[KW15] [KW15] Kitchloo, N. and Wilson, W. S., The ER(n)-cohomology of BO(q) and real Johnson-Wilson orientations for vector bundles. Bull. Lond. Math. Soc. 47(2015), 835–847. http://dx.doi.Org/10.1112/blms/bdvO57 Google Scholar

[Lan70] [Lan70] Landweber, P. S., Coherence, flatness and cobordism of classifying spaces. In: Proceedings of Advanced Study Institute on Algebraic Topology, Mat. Inst., Aarhus, 1970, pp. 256–269. Google Scholar

[Lor16] [Lor16] Lorman, V., The real Johnson-Wilson cohomology ℂℙ∞. Topology Appl. 209(2016), 367–388. Google Scholar | DOI

Cité par Sources :