Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 026, 19 pages      arXiv:1408.1555      https://doi.org/10.3842/SIGMA.2016.026

Basic Forms and Orbit Spaces: a Diffeological Approach

Yael Karshon a and Jordan Watts b
a) Department of Mathematics, University of Toronto, 40 St. George Street, Toronto Ontario M5S 2E4, Canada
b) Department of Mathematics, University of Colorado Boulder, Campus Box 395, Boulder, CO, 80309, USA

Received October 06, 2015, in final form February 16, 2016; Published online March 08, 2016

Abstract
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.

Key words: diffeology; Lie group actions; orbit space; basic differential forms.

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