TY - JOUR
T1 - Basic forms and orbit spaces
T2 - A diffeological approach
AU - Karshon, Yael
AU - Watts, Jordan
N1 - Publisher Copyright:
© 2016, Institute of Mathematics. All rights reserved.
PY - 2016/3/8
Y1 - 2016/3/8
N2 - If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential forms in the diffeological sense.
AB - If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential forms in the diffeological sense.
KW - Basic differential forms
KW - Diffeology
KW - Lie group actions
KW - Orbit space
UR - http://www.scopus.com/inward/record.url?scp=84960445005&partnerID=8YFLogxK
U2 - 10.3842/SIGMA.2016.026
DO - 10.3842/SIGMA.2016.026
M3 - Article
AN - SCOPUS:84960445005
SN - 1815-0659
VL - 12
JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
M1 - 026
ER -