scholarly journals Algebraic models for equivariant homotopy theory over Abelian compact Lie groups

2002 ◽  
Vol 240 (2) ◽  
pp. 261-287 ◽  
Author(s):  
Michael A. Mandell ◽  
Laura Scull
Keyword(s):  
Lie Groups ◽  
Homotopy Theory ◽  
Equivariant Homotopy ◽  
Algebraic Models ◽  
Compact Lie Groups ◽  
Equivariant Homotopy Theory

Translation Groupoids and Orbifold Cohomology

2010 ◽  
Vol 62 (3) ◽  
pp. 614-645 ◽  
Author(s):  
Dorette Pronk ◽  
Laura Scull
Keyword(s):  
Equivariant Cohomology ◽  
Homotopy Theory ◽  
Equivariant Homotopy ◽  
Equivariant Maps ◽  
Bredon Cohomology ◽  
Orbifold Cohomology ◽  
Equivariant Homotopy Theory

AbstractWe 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.

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