Unstable splittings for real spectra
Algebraic and Geometric Topology, Tome 13 (2013) no. 2, pp. 1053-1070
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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.

DOI : 10.2140/agt.2013.13.1053
Classification : 55N20, 55N22, 55N91
Keywords: unstable homotopy, unstable splitting, real spectra

Kitchloo, Nitu  1   ; Wilson, W Stephen  1

1 Department of Mathematics, Johns Hopkins University, 3400 N. Charles St., Baltimore, MD 21218, USA
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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] J M Boardman, D C Johnson, W S Wilson, Unstable operations in generalized cohomology, from: "Handbook of algebraic topology" (editor I James), North-Holland (1995) 687

[2] J M Boardman, W S Wilson, 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] D M Davis, A strong nonimmersion theorem for real projective spaces, Ann. of Math. 120 (1984) 517

[4] M A Hill, M J Hopkins, D C Ravenel, On the non-existence of elements of Kervaire invariant one

[5] P Hu, On Real-oriented Johnson–Wilson cohomology, Algebr. Geom. Topol. 2 (2002) 937

[6] P Hu, I Kriz, Real-oriented homotopy theory and an analogue of the Adams–Novikov spectral sequence, Topology 40 (2001) 317

[7] N Kitchloo, W S Wilson, 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] N Kitchloo, W S Wilson, On the Hopf ring for $ER(n)$, Topology Appl. 154 (2007) 1608

[9] N Kitchloo, W S Wilson, The second real Johnson–Wilson theory and nonimmersions of $RP^n$, Homology, Homotopy Appl. 10 (2008) 223

[10] N Kitchloo, W S Wilson, The second real Johnson–Wilson theory and nonimmersions of $RP^n$. II, Homology, Homotopy Appl. 10 (2008) 269

[11] M Mahowald, C Rezk, Topological modular forms of level 3, Pure Appl. Math. Q. 5 (2009) 853

[12] W S Wilson, The $\Omega $–spectrum for Brown–Peterson cohomology. II, Amer. J. Math. 97 (1975) 101

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