120 research outputs found
The Lusternik-Schnirelmann Category for a Differentiable Stack
No full textWe introduce the notion of Lusternik-Schnirelmann category for differentiable stacks and establish its relation with the groupoid Lusternik-Schnirelmann category for Lie groupoids. This extends the notion of Lusternik-Schnirelmann category for smooth manifolds and orbifolds
Morita Invariance of Invariant Topological Complexity
No full textWe show that the invariant topological complexity defines a new numerical invariant for orbifolds.
Orbifolds may be described as global quotients of spaces by compact group actions with finite isotropy groups. The same orbifold may have descriptions involving different spaces and different groups. We say that two actions are Morita equivalent if they define the same orbifold. Therefore, any notion defined for group actions should be Morita invariant to be well defined for orbifolds.
We use the homotopy invariance of equivariant principal bundles to prove that the equivariant A-category of Clapp and Puppe is invariant under Morita equivalence. As a corollary, we obtain that both the equivariant Lusternik-Schnirelmann category of a group action and the invariant topological complexity are invariant under Morita equivalence. This allows a definition of topological complexity for orbifolds.
This is joint work with Andres Angel, Mark Grant and John OpreaNon UBCUnreviewedAuthor affiliation: Wright CollegeFacult
Transverse Lusternik–Schnirelmann category of Riemannian foliations
No full textAbstractThe transverse Lusternik–Schnirelmann category of a foliation is an invariant of foliated homotopy type. In this paper we show that the category of a Riemannian foliation is infinite if there exists a non-compact leaf verifying certain conditions. Examples of the obstruction to construct categorical coverings in such foliations are given
G-category versus orbifold category
No full textWe present a comparative study of certain invariants defined for group actions and
their analogues defined for orbifolds. In particular, we prove that Fadell's equivariant
category for -spaces coincides with the Lusternik-Schnirelmann category for
orbifolds when the group is finite
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