Basic Forms and Orbit Spaces: a Diffeological Approach
Copyright policy )Basic Forms and Orbit Spaces: a Diffeological Approach
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.
- University of Colorado Boulder United States
- University of Nebraska-Lincoln United States
- Central Michigan University United States
- University of Toronto Canada
lie group actions, Mathematics - Differential Geometry, Lie group actions, Natural Resources Management and Policy, Geometric Topology (math.GT), 58D19, 57R99, Mathematics - Geometric Topology, Differential topology, Differential Geometry (math.DG), diffeology, Mathematics - Symplectic Geometry, Natural Resources and Conservation, FOS: Mathematics, Group actions and symmetry properties, Symplectic Geometry (math.SG), basic differential forms, Other Environmental Sciences, Environmental Sciences, orbit space
lie group actions, Mathematics - Differential Geometry, Lie group actions, Natural Resources Management and Policy, Geometric Topology (math.GT), 58D19, 57R99, Mathematics - Geometric Topology, Differential topology, Differential Geometry (math.DG), diffeology, Mathematics - Symplectic Geometry, Natural Resources and Conservation, FOS: Mathematics, Group actions and symmetry properties, Symplectic Geometry (math.SG), basic differential forms, Other Environmental Sciences, Environmental Sciences, orbit space
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