The equivariant Euler characteristic

Steven R. Costenoble, Stefan Waner, Yihren Wu
1991 Journal of Pure and Applied Algebra  
Costenoble, S.R., S. Waner and Y. Wu, The equib riant Euler characteristic, Journal of Pure and Applied Algebra 70 (1991) 227-249. We describe an equivariant version of the Euler characteristic in order to extend to the equivariant case classical results relating the Euler characteristic to vector field (Reinhart) bordism of smooth manifolds and controllable cut-and-paste equivalence. We show that the nonequivariant results continue to hold for an arbitrary finite ambient group G, both in the
more » ... iented and unoriented cases, and thereby extend work on this subject begun by several authors. We use a new definition of equivariant orientation in terms of a categorical notion of 'groupoid representations'. 0022-4049/91/$03,50 0 1991 -Elsevier Science Publishers B.V. (North-Holland)
doi:10.1016/0022-4049(91)90071-9 fatcat:xj2ebjdenrcgbi2vnjyzvmw2pe