Introduction to Foliations and Lie Groupoids: Prerequisites

By Ieke Moerdijk, J. Mrčun. 2003

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View Paper: https://www.semanticscholar.org/paper/9cdeaea8ecebbcaa97d6724425b1b9bca992f0ce

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Citations in the corpus

Orbifolds as stacks (2008, unknown): “I have mostly cribbed from Moerdijk-Mrčun [19].”
Geometry of orbit spaces of proper Lie groupoids (2010, background): “up action on a manifold, the deﬁnition above yields the basic cohomology of a quotient space, as in [Kos]. ii) A Lie groupoid Gis a foliation groupoid when the anchorof its Lie algebroid is injective [MoMr]. In this case one ﬁnds the basic cohomology of the leaf space of the associated foliation, de”
A General Fredholm Theory and Applications (2005, methodology): “Clearly, the notion of a polyfold groupoid is a straightforward modification of that of a Lie groupoid, where we have replaced the notion of a finite-dimensional manifold by that of a M-polyfold and the notion of submersion is modified by that of a fred-submersion; see [32, 33].”
Hořava gravity at a Lifshitz point: A progress report (2017, background): “3), and forms an independent branch of differential geometry [76].”
A general Fredholm theory I: A splicing-based differential geometry (2006, background): “The third paper, [11], develops the Fredholm theory in polyfolds, which could be viewed as a theory of Fredholm functors in a version of Lie groupoids with object and morphism spaces build on the new local models (see [20],[21] for the groupoid concepts in a manifold world).”
Cosmology of the Lifshitz universe (2009, background): “, diffeomorphisms preserving the codimension-one foliation of M [86] with leaves Σ.”
Differentiable stacks and gerbes (2006, background): “Furthermore, we assume that X1 ⇒ X0 is a Hausdorff and second countable Lie groupoid [28, 38].”
Ehresmann doubles and Drinfel'd doubles for Lie algebroids and Lie bialgebroids (2006, background): “The paper is arranged so that §2 to §6 will be self-contained for a reader who is familiar with the basics of Lie algebroids [35], Chapter 3, [44], Chapter 6, and Poisson geometry [52], [9] and who is willing to pick up the language of double vector bundles from §2 and [35], Chapter 9.”
On the universal enveloping algebra of a Lie algebroid (2010, background): “In this section we will briefly recall the definition of Lie algebroids and mention some basic examples (see [9, 12] for more details, examples and historical remarks).”
The Weil algebra and the Van Est isomorphism (2009, methodology): “First of all, the classical Weil algebra W (g) associated to a Lie group G (or, better, to its Lie algebra g) arises as the algebraic model for the “DeRham complex” of the total space EG [6] (see also [12, 11]).”
PROPER GROUPOIDS AND MOMENTUM MAPS: LINEARIZATION, AFFINITY, AND CONVEXITY GROUPOPROPRES ET APPLICATIONS MOMENT: LIN ´ EARISATION, CARACT ` ERE AFFINE, ET CONVEXIT ´ E (2004, background): “A sketchy proof of point iv) can be found in [21], Chapter on Lie groupoids.”
On Quasitoric Orbifolds (2008, unknown): “The reader may also consult [14] for an excellent exposition of the foundations of the theory of (reduced) differentiable orbifolds.”