1. CJM 2009 (vol 62 pp. 614)
|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 2004 (vol 56 pp. 1290)
|Equivariant Formality for Actions of Torus Groups |
This paper contains a comparison of several definitions of equivariant formality for actions of torus groups. We develop and prove some relations between the definitions. Focusing on the case of the circle group, we use $S^1$-equivariant minimal models to give a number of examples of $S^1$-spaces illustrating the properties of the various definitions.
Keywords:Equivariant homotopy, circle action, minimal model,, rationalization, formality
Categories:55P91, 55P62, 55R35, 55S45