We show that the unstable splittings of the spaces in the Omega spectra representing BP, BP〈n〉 and E(n) from [Amer. J. Math. 97 (1975) 101–123] may be obtained for the real analogs of these spectra using techniques similar to those in [Progr. Math. 196 (2001) 35–45]. Explicit calculations for ER(2) are given.
Keywords: unstable homotopy, unstable splitting, real spectra
Kitchloo, Nitu  1 ; Wilson, W Stephen  1
@article{10_2140_agt_2013_13_1053,
author = {Kitchloo, Nitu and Wilson, W Stephen},
title = {Unstable splittings for real spectra},
journal = {Algebraic and Geometric Topology},
pages = {1053--1070},
year = {2013},
volume = {13},
number = {2},
doi = {10.2140/agt.2013.13.1053},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.1053/}
}
TY - JOUR AU - Kitchloo, Nitu AU - Wilson, W Stephen TI - Unstable splittings for real spectra JO - Algebraic and Geometric Topology PY - 2013 SP - 1053 EP - 1070 VL - 13 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2013.13.1053/ DO - 10.2140/agt.2013.13.1053 ID - 10_2140_agt_2013_13_1053 ER -
Kitchloo, Nitu; Wilson, W Stephen. Unstable splittings for real spectra. Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 1053-1070. doi: 10.2140/agt.2013.13.1053
[1] , , , Unstable operations in generalized cohomology, from: "Handbook of algebraic topology" (editor I James), North-Holland (1995) 687
[2] , , Unstable splittings related to Brown–Peterson cohomology, from: "Cohomological methods in homotopy theory" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 35
[3] , A strong nonimmersion theorem for real projective spaces, Ann. of Math. 120 (1984) 517
[4] , , , On the non-existence of elements of Kervaire invariant one
[5] , On Real-oriented Johnson–Wilson cohomology, Algebr. Geom. Topol. 2 (2002) 937
[6] , , Real-oriented homotopy theory and an analogue of the Adams–Novikov spectral sequence, Topology 40 (2001) 317
[7] , , On fibrations related to real spectra, from: "Proceedings of the Nishida Fest" (editors M Ando, N Minami, J Morava, W Wilson), Geom. Topol. Monogr. 10, Geom. Topol. Publ., Coventry (2007) 237
[8] , , On the Hopf ring for $ER(n)$, Topology Appl. 154 (2007) 1608
[9] , , The second real Johnson–Wilson theory and nonimmersions of $RP^n$, Homology, Homotopy Appl. 10 (2008) 223
[10] , , The second real Johnson–Wilson theory and nonimmersions of $RP^n$. II, Homology, Homotopy Appl. 10 (2008) 269
[11] , , Topological modular forms of level 3, Pure Appl. Math. Q. 5 (2009) 853
[12] , The $\Omega $–spectrum for Brown–Peterson cohomology. II, Amer. J. Math. 97 (1975) 101
Cité par Sources :