Journal ArticleDOI
On essential conformal groups and a conformal invariant
TLDR
In this paper, it was shown that various conformal groups, including classical conformal diffeomorphism groups, are essential and that their essentiality is equivalent to the non-vanishing of a conformal cohomological invariant.Abstract:
We show that various conformal groups, including classical conformal diffeomorphism groups are essential. The essentiality is shown to be equivalent to the non-vanishing of a conformal cohomological invariant.read more
Citations
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Journal ArticleDOI
Some properties of locally conformal symplectic structures
TL;DR: In this article, it was shown that the conformally invariant usual de Rham cohomology of an appropriate cover is isomorphic to the locally conformal symplectic (lcs) cohomology.
Journal ArticleDOI
Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
Stefan Müller,Peter Spaeth +1 more
TL;DR: In this paper, the authors introduce topological contact dynamics of a smooth manifold carrying a cooriented contact structure, generalizing previous work in the case of a symplectic structure [MO07] or a contact form [BS12].
Journal ArticleDOI
Crossed product extensions of spectral triples
Bruno Iochum,Thierry Masson +1 more
TL;DR: In this paper, a spectral triple was extended to a triplet on the crossed product of the affine group and the conformal group acting on a complete Riemannian spin manifold, which can be promoted to a modular-type twisted spectral triple within a general procedure.
Journal ArticleDOI
Tangent Maps and Tangent Groupoid for Carnot Manifolds
Woocheol Choi,Raphael Ponge +1 more
TL;DR: In this article, the authors introduce a notion of differential, called Carnot differential, for maps that are compatible with the Carnot manifold structure, which is obtained as a group map between the corresponding tangent groups.
Journal ArticleDOI
Noncommutative geometry and conformal geometry. I. Local index formula and conformal invariants
Raphael Ponge,Hang Wang +1 more
TL;DR: In this article, a local index formula in conformal-diffeomorphism invariant geometry was established, and a huge class of global conformal invariants taking into account the action of the group of conformal diffeomorphisms was constructed.
References
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Book
A Course in Homological Algebra
Peter Hilton,Urs Stammbach +1 more
TL;DR: In this paper, the authors propose an extension of the Kunneth Theorem for Abelian groups, which is based on the notion of double complexes, and they use it to define the (co-)homology of groups.
Journal ArticleDOI
Invariants of contact structures and transversally oriented foliations
TL;DR: In this article, the transverse Calabi invariants of the contact structure E(α), the contact flow Fα and the transversal symplectic geometry of a contact manifold (M, α) were introduced.