TY - JOUR
T1 - K-theory and homotopies of 2-cocycles on transformation groups
AU - Gillaspy, Elizabeth
N1 - Publisher Copyright:
© by THETA, 2015.
PY - 2015
Y1 - 2015
N2 - This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles w = {wt}tε[0,1] on a locally compact Hausdorff groupoid G induces an isomorphism of the Ktheory groups of the reduced twisted groupoid C*-algebras: Generalizing work of S. Echterhoff, W. Lück, N.C. Phillips, S. Walters, J. Reine Angew. Math. 639(2010), 173-221, we show that if G = G ⋉ X is a transformation group such that G satisfies the Baum-Connes conjecture with coefficients, a homotopy w = {wt}tε[0,1] of 2-cocycles on G ⋉ X gives rise to an isomorphism.
AB - This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles w = {wt}tε[0,1] on a locally compact Hausdorff groupoid G induces an isomorphism of the Ktheory groups of the reduced twisted groupoid C*-algebras: Generalizing work of S. Echterhoff, W. Lück, N.C. Phillips, S. Walters, J. Reine Angew. Math. 639(2010), 173-221, we show that if G = G ⋉ X is a transformation group such that G satisfies the Baum-Connes conjecture with coefficients, a homotopy w = {wt}tε[0,1] of 2-cocycles on G ⋉ X gives rise to an isomorphism.
KW - 2-cocycle
KW - Groupoid
KW - K-theory
KW - Transformation group
KW - Twisted groupoid C-algebra
UR - http://www.scopus.com/inward/record.url?scp=84929244684&partnerID=8YFLogxK
U2 - 10.7900/jot.2014feb14.2033
DO - 10.7900/jot.2014feb14.2033
M3 - Article
AN - SCOPUS:84929244684
SN - 0379-4024
VL - 73
SP - 465
EP - 490
JO - Journal of Operator Theory
JF - Journal of Operator Theory
IS - 2
ER -