TY - JOUR
T1 - K-theory and homotopies of 2-cocycles on group bundles
AU - Gillaspy, Elizabeth
N1 - Publisher Copyright:
Copyright ©2016 Rocky Mountain Mathematics Consortium.
PY - 2016
Y1 - 2016
N2 - This paper continues the author's program of investigating the question of when a homotopy of 2-cocycles Ω = {ωt}t∈[0,1] on a locally compact Hausdorff groupoid G induces an isomorphism of the K-theory groups of the twisted groupoid C∗-algebras: K∗(C∗(G, ω0)) ≅ K∗(C∗(G, ω1)). Building on our earlier work in [4, 5], we show that, if π : G → M is a locally trivial bundle of amenable groups over a locally compact Hausdorff space M, a homotopy Ω = {ωt}t∈[0,1] of 2-cocycles on G gives rise to an isomorphism: K∗(C∗(G, ω0)) ≅ K∗(C∗(G, ω1)).
AB - This paper continues the author's program of investigating the question of when a homotopy of 2-cocycles Ω = {ωt}t∈[0,1] on a locally compact Hausdorff groupoid G induces an isomorphism of the K-theory groups of the twisted groupoid C∗-algebras: K∗(C∗(G, ω0)) ≅ K∗(C∗(G, ω1)). Building on our earlier work in [4, 5], we show that, if π : G → M is a locally trivial bundle of amenable groups over a locally compact Hausdorff space M, a homotopy Ω = {ωt}t∈[0,1] of 2-cocycles on G gives rise to an isomorphism: K∗(C∗(G, ω0)) ≅ K∗(C∗(G, ω1)).
KW - 2-cocycle
KW - Group bundle
KW - K-theory
KW - Twisted groupoid C∗-algebra
UR - http://www.scopus.com/inward/record.url?scp=84991810138&partnerID=8YFLogxK
U2 - 10.1216/RMJ-2016-46-4-1207
DO - 10.1216/RMJ-2016-46-4-1207
M3 - Article
AN - SCOPUS:84991810138
SN - 0035-7596
VL - 46
SP - 1207
EP - 1229
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
IS - 4
ER -