Volume 10 (2007)

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On fibrations related to real spectra

Nitu Kitchloo and W Stephen Wilson

Geometry & Topology Monographs 10 (2007) 237–244

DOI: 10.2140/gtm.2007.10.237

arXiv: 0903.4602

Abstract

We consider real spectra, collections of Z/(2)–spaces indexed over ZZα with compatibility conditions. We produce fibrations connecting the homotopy fixed points and the spaces in these spectra. We also evaluate the map which is the analogue of the forgetful functor from complex to reals composed with complexification. Our first fibration is used to connect the real 2n+2(2n-1)–periodic Johnson–Wilson spectrum ER(n) to the usual 2(2n-1)–periodic Johnson–Wilson spectrum, E(n). Our main result is the fibration Σλ(n)ER(n)→ER(n)→E(n), where λ(n)=22n+1-2n+2+1.

Keywords

homotopy fixed points, real complex cobordism

Mathematical Subject Classification

Primary: 55N20, 55Q51, 55R45

References
Publication

Received: 24 June 2004
Revised: 11 September 2005
Published: 27 January 2007

Authors
Nitu Kitchloo
Department of Mathematics
University of California, San Diego
La Jolla CA 92093-0112
USA
W Stephen Wilson
Department of Mathematics
Johns Hopkins University
Baltimore MD 21218
USA