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Search: MSC category 19L47 ( Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91] )

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1. 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

2. CJM 2001 (vol 53 pp. 3)

Bell, J. P.
The Equivariant Grothendieck Groups of the Russell-Koras Threefolds
The Russell-Koras contractible threefolds are the smooth affine threefolds having a hyperbolic $\mathbb{C}^*$-action with quotient isomorphic to the corresponding quotient of the linear action on the tangent space at the unique fixed point. Koras and Russell gave a concrete description of all such threefolds and determined many interesting properties they possess. We use this description and these properties to compute the equivariant Grothendieck groups of these threefolds. In addition, we give certain equivariant invariants of these rings.

Categories:14J30, 19L47

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