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A simple characterisation of topological amenability in terms of bounded cohomology is proved, following Johnson's formulation of amenability. The connection to injective Banach modules is established.
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In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely additive measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English) in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun on "mean".
In mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of a coordinate frame, and so is not a tensorial object.
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups, usually one associated with a topological space, often defined from a cochain complex. Cohomology can be viewed as a method of assigning richer algebraic invariants to a space than homology. Some versions of cohomology arise by dualizing the construction of homology. In other words, cochains are functions on the group of chains in homology theory.
Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).
We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of orientation-preserving homeomorphisms of the circle and of the closed 2-disc, it is isomorphic to the polynomial ring g ...
The bridge over the Venoge, built in 1966 and extended in 1997, is a composite bridge located on the highway between Lausanne and Geneva. The aim of this thesis will be to develop a digital twin of this bridge, which consist of a digital representation as ...
Roughness, defined as unevenness of material surfaces, plays an important role in determining how engineering components or natural objects interact with other bodies and their environment. The emergence of fractal roughness on natural and engineered surfa ...