64,801 research outputs found
Poisson varieties from Riemann surfaces
Short survey based on talk at the Poisson 2012 conference. The main aim is to
describe and give some examples of wild character varieties (naturally
generalising the character varieties of Riemann surfaces by allowing more
complicated behaviour at the boundary), their Poisson/symplectic structures
(generalising both the Atiyah-Bott approach and the quasi-Hamiltonian
approach), and the wild mapping class groups.Comment: 33 pages, 3 figure
The Structure and Interpretation of Cosmology: Part I - General Relativistic Cosmology
The purpose of this work is to review, clarify, and critically analyse modern
mathematical cosmology. The emphasis is upon mathematical objects and
structures, rather than numerical computations. This paper concentrates on
general relativistic cosmology. The opening section reviews and clarifies the
Friedmann-Robertson-Walker models of general relativistic cosmology, while
Section 2 deals with the spatially homogeneous models. Particular attention is
paid in these opening sections to the topological and geometrical aspects of
cosmological models. Section 3 explains how the mathematical formalism can be
linked with astronomical observation. In particular, the informal,
observational notion of the celestial sphere is given a rigorous mathematical
implementation. Part II of this work will concentrate on inflationary cosmology
and quantum cosmology
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