Symplectic Actions of $2$-Tori on $4$-Manifolds PDF Download
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Author: Alvaro Pelayo
Publisher: American Mathematical Soc.
ISBN: 0821847139
Category : Mathematics
Languages : en
Pages : 96
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Book Description
In this paper the author classifies symplectic actions of $2$-tori on compact connected symplectic $4$-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The classification is in terms of a collection of invariants of the topology of the manifold, of the torus action and of the symplectic form. The author constructs explicit models of such symplectic manifolds with torus actions, defined in terms of these invariants.
Author: Alvaro Pelayo
Publisher: American Mathematical Soc.
ISBN: 0821847139
Category : Mathematics
Languages : en
Pages : 96
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Book Description
In this paper the author classifies symplectic actions of $2$-tori on compact connected symplectic $4$-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The classification is in terms of a collection of invariants of the topology of the manifold, of the torus action and of the symplectic form. The author constructs explicit models of such symplectic manifolds with torus actions, defined in terms of these invariants.
Author: Michèle Audin
Publisher: Birkhäuser
ISBN: 3034872216
Category : Mathematics
Languages : en
Pages : 181
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Book Description
The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity results, it contains much more material, in particular lots of new examples and exercises.
Author: Michèle Audin
Publisher: Birkhäuser
ISBN: 3034879601
Category : Mathematics
Languages : en
Pages : 331
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Book Description
The material and references in this extended second edition of "The Topology of Torus Actions on Symplectic Manifolds", published as Volume 93 in this series in 1991, have been updated. Symplectic manifolds and torus actions are investigated, with numerous examples of torus actions, for instance on some moduli spaces. Although the book is still centered on convexity results, it contains much more material, in particular lots of new examples and exercises.
Author: Klaus Thomsen
Publisher: American Mathematical Soc.
ISBN: 0821846922
Category : Mathematics
Languages : en
Pages : 138
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Book Description
The author unifies various constructions of $C^*$-algebras from dynamical systems, specifically, the dimension group construction of Krieger for shift spaces, the corresponding constructions of Wagoner and Boyle, Fiebig and Fiebig for countable state Markov shifts and one-sided shift spaces, respectively, and the constructions of Ruelle and Putnam for Smale spaces. The general setup is used to analyze the structure of the $C^*$-algebras arising from the homoclinic and heteroclinic equivalence relations in expansive dynamical systems, in particular, expansive group endomorphisms and automorphisms and generalized 1-solenoids. For these dynamical systems it is shown that the $C^*$-algebras are inductive limits of homogeneous or sub-homogeneous algebras with one-dimensional spectra.
Author: Montserrat Casals-Ruiz
Publisher: American Mathematical Soc.
ISBN: 0821852582
Category : Mathematics
Languages : en
Pages : 168
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Book Description
"Volume 212, number 999 (end of volume)."
Author: Ana Cannas da Silva
Publisher: Springer
ISBN: 354045330X
Category : Mathematics
Languages : en
Pages : 240
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Book Description
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Author: Olivier Alvarez
Publisher: American Mathematical Soc.
ISBN: 0821847155
Category : Mathematics
Languages : en
Pages : 90
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Book Description
"Volume 204, number 960 (fourth of 5 numbers)."
Author: Makoto Sakai
Publisher: American Mathematical Soc.
ISBN: 0821848100
Category : Mathematics
Languages : en
Pages : 282
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Book Description
For a given plane domain, the author adds a constant multiple of the Dirac measure at a point in the domain and makes a new domain called a quadrature domain. The quadrature domain is characterized as a domain such that the integral of a harmonic and integrable function over the domain equals the integral of the function over the given domain plus the integral of the function with respect to the added measure. The family of quadrature domains can be modeled as the Hele-Shaw flow with a free-boundary problem. The given domain is regarded as the initial domain and the support point of the Dirac measure as the injection point of the flow.
Author: Daniel Allcock
Publisher: American Mathematical Soc.
ISBN: 0821847511
Category : Mathematics
Languages : en
Pages : 89
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Book Description
"Volume 209, number 985 (fourth of 5 numbers)."
Author: Mark P. Walsh
Publisher: American Mathematical Soc.
ISBN: 082185304X
Category : Mathematics
Languages : en
Pages : 105
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Book Description
It is well known that isotopic metrics of positive scalar curvature are concordant. Whether or not the converse holds is an open question, at least in dimensions greater than four. The author shows that for a particular type of concordance, constructed using the surgery techniques of Gromov and Lawson, this converse holds in the case of closed simply connected manifolds of dimension at least five.
