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Search: MSC category 55N20 ( Generalized (extraordinary) homology and cohomology theories )

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1. CJM Online first

Kitchloo, Nitu; Lorman, Vitaly; Wilson, W. Stephen
The $ER(2)$-cohomology of $B\mathbb{Z}/(2^q)$ and $\mathbb{C} \mathbb{P}^n$
The $ER(2)$-cohomology of $B\mathbb{Z}/(2^q)$ and $\mathbb{C}\mathbb{P}^n$ are computed along with the Atiyah-Hirzebruch spectral sequence for $ER(2)^*(\mathbb{C}\mathbb{P}^\infty)$. This, along with other papers in this series, gives us the $ER(2)$-cohomology of all Eilenberg-MacLane spaces.

Keywords:complex projective space, cohomology theory, Eilenberg-MacLane space, Atiyah-Hirzebruch spectral sequence
Categories:55N20, 55N91, 55P20, 55T25

2. CJM 2015 (vol 68 pp. 463)

Sadykov, Rustam
The Weak b-principle: Mumford Conjecture
In this note we introduce and study a new class of maps called oriented colored broken submersions. This is the simplest class of maps that satisfies a version of the b-principle and in dimension $2$ approximates the class of oriented submersions well in the sense that every oriented colored broken submersion of dimension $2$ to a closed simply connected manifold is bordant to a submersion. We show that the Madsen-Weiss theorem (the standard Mumford Conjecture) fits a general setting of the b-principle. Namely, a version of the b-principle for oriented colored broken submersions together with the Harer stability theorem and Miller-Morita theorem implies the Madsen-Weiss theorem.

Keywords:generalized cohomology theories, fold singularities, h-principle, infinite loop spaces
Categories:55N20, 53C23

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