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Search: MSC category 55N91 ( Equivariant homology and cohomology [See also 19L47] )

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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 2009 (vol 62 pp. 614)

Pronk, Dorette; Scull, Laura
Translation Groupoids and Orbifold Cohomology
We show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps, giving a mechanism for transferring results from equivariant homotopy theory to the orbifold category. As an application, we use this result to define orbifold versions of a couple of equivariant cohomology theories: K-theory and Bredon cohomology for certain coefficient diagrams.

Keywords:orbifolds, equivariant homotopy theory, translation groupoids, bicategories of fractions
Categories:57S15, 55N91, 19L47, 18D05, 18D35

3. CJM 2009 (vol 62 pp. 473)

Yun, Zhiwei
Goresky—MacPherson Calculus for the Affine Flag Varieties
We use the fixed point arrangement technique developed by Goresky and MacPherson to calculate the part of the equivariant cohomology of the affine flag variety $\mathcal{F}\ell_G$ generated by degree 2. We use this result to show that the vertices of the moment map image of $\mathcal{F}\ell_G$ lie on a paraboloid.

Categories:14L30, 55N91

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