Subgroup Of Diffeomorphisms Research Articles

Henneaux–Teitelboim Gauge Symmetry and Its Applications to Higher Gauge Theories

When discussing the gauge symmetries of any theory, the Henneaux–Teitelboim transformations are often underappreciated or even completely ignored, due to their on-shell triviality. Nevertheless, these gauge transformations play an important role in understanding the structure of the full gauge symmetry group of any theory, especially regarding the subgroup of diffeomorphisms. We give a review of the Henneaux–Teitelboim transformations and the resulting gauge group in the general case and then discuss its role in the applications to the class of topological theories called nBF models, relevant for the constructions of higher gauge theories and quantum gravity.

Topology of Foliations and Decomposition of Stochastic Flows of Diffeomorphisms

Let M be a compact manifold equipped with a pair of complementary foliations, say horizontal and vertical. In Catuogno et al. (Stoch Dyn 13(4):1350009, 2013) it is shown that, up to a stopping time $$\tau $$ , a stochastic flow of local diffeomorphisms $$\varphi _t$$ in M can be written as a Markovian process in the subgroup of diffeomorphisms which preserve the horizontal foliation composed with a process in the subgroup of diffeomorphisms which preserve the vertical foliation. Here, we discuss topological aspects of this decomposition. The main result guarantees the global decomposition of a flow if it preserves the orientation of a transversely orientable foliation. In the last section, we present an Ito-Liouville formula for subdeterminants of linearised flows. We use this formula to obtain sufficient conditions for the existence of the decomposition for all $$t\ge 0$$ .

Normal subgroups of diffeomorphism and homeomorphism groups of ℝn and other open manifolds

AbstractWe determine all the normal subgroups of the group of Cr diffeomorphisms of ℝn, 1≤r≤∞, except when r=n+1 or n=4, and also of the group of homeomorphisms of ℝn ( r=0). We also study the group A0 of diffeomorphisms of an open manifold M that are isotopic to the identity. If M is the interior of a compact manifold with non-empty boundary, then the quotient of A0 by the normal subgroup of diffeomorphisms that coincide with the identity near to a given end e of M is simple.

On action of diffeomorphisms of C*-algebras on derivations

In this paper we consider automorphisms of the domains of closed *-derivations of C*-algebras and show that they extend to automorphisms of C*-algebras, so we call them diffeomorphisms. The diffeomorphisms generate transformations of the sets of closed *-derivations of C*-algebras. In this paper we study the subgroups of diffeomorphisms that define “bounded” shifts of derivations and the subgroups of the stabilizers of derivations.

On the second homology group of the discrete group of diffeomorphisms of the circle

Let G be the discrete group of orientation preserving diffeomorphisms of the circle, and let H be the subgroup of diffeomorphisms which are the identity in a neighborhood of a given point. It is proved that there is a short exact sequence in the integral homology of groups 0→H 2(H)→H 2(G) → E Z→0 . The epimorphism E can be identified with the Euler class for transversally foliated circle bundles. The sequence has a natural interpretation in terms of cobordism classes of foliated bundles with Euler class equal to 0.