# On Real-oriented Johnson–Wilson cohomology

@article{Hu2002OnRJ, title={On Real-oriented Johnson–Wilson cohomology}, author={Po Hu}, journal={Algebraic \& Geometric Topology}, year={2002}, volume={2}, pages={937-947} }

Answering a question of W. S. Wilson, I introduce a Z=2- equivariant Atiyah-Real analogue of Johnson-Wilson cohomology theory BPhni, whose coecient ring is the n-chromatic part of Landweber's Real cobordism ring. AMS Classication 55P42, 55P91; 55T25

## 9 Citations

The representation-ring-graded local cohomology spectral sequence for BPℝ⟨3⟩

- Mathematics
- 2017

Abstract The purpose of this paper is to examine the calculational consequences of the duality proved by the first author and Meier in [13], making them explicit in one more example. We give an…

On fibrations related to real spectra

- Mathematics
- 2007

We consider real spectra, collections of Z=(2)–spaces indexed over Z Z withcompatibility conditions. We produce ﬁbrations connecting the homotopy ﬁxedpointsandthespacesinthesespectra.…

A modular description of ER(2)

- Mathematics
- 2012

We give a description of the maximally unramified extension of completed second Real Johnson-Wilson theory using supersingular elliptic curves with $\Gamma_0(3)$-level structures.

Gorenstein duality for Real spectra

- Mathematics
- 2016

Following Hu and Kriz, we study the $C_2$-spectra $BP\mathbb{R}\langle n \rangle$ and $E\mathbb{R}(n)$ that refine the usual truncated Brown-Peterson and the Johnson-Wilson spectra. In particular, we…

On the ER(2)-cohomology of some odd-dimensional projective spaces

- Mathematics
- 2012

Abstract Kitchloo and Wilson have used the homotopy fixed points spectrum ER ( 2 ) of the classical complex-oriented Johnson–Wilson spectrum E ( 2 ) to deduce certain non-immersion results for real…

Unstable splittings for real spectra

- Mathematics
- 2013

We show that the unstable splittings of the spaces in the Omega spectra representing BP , BPhni and E.n/ from [12] may be obtained for the real analogs of these spectra using techniques similar to…

On the Hopf ring for ER(n)

- Mathematics
- 2007

Abstract Kriz and Hu construct a real Johnson–Wilson spectrum, ER ( n ) , which is 2 n + 2 ( 2 n − 1 ) periodic. ER ( 1 ) is just KO ( 2 ) . We do two things in this paper. First, we compute the…

Galois descent for real spectra

- Mathematics
- 2013

We prove analogs of faithfully flat descent and Galois descent for categories of modules over $$E_{\infty }$$E∞-ring spectra using the $$\infty $$∞-categorical Barr-Beck theorem proved by Lurie. In…

Tate blueshift and vanishing for Real oriented cohomology

- Mathematics
- 2019

Ando, Morava, and Sadofsky showed that the Tate construction for a trivial $\mathbb{Z}/p$-action decreases the chromatic height of Johnson-Wilson theory, and Greenlees and Sadofsky proved that the…

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Using the Landweber}Araki theory of Real cobordism and Real-oriented spectra, we de"ne a Real analogue of the Adams}Novikov spectral sequence. This is a new spectral sequence with a potentially…

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The last decade has seen a great deal of activity in this area. The chapter provides a brief sketch of the basic concepts of space-level equivariant homotopy theory. It also provides an introduction…