A Glimpse at Set Theory. The Real Numbers. The Topology of Cartesian Spaces. Convergence. Continuous Functions. Functions of One Variable. Infinite Series. Differentiation in RP Integration in RP.

The elements of real analysis (2nd edition), by Robert G. Bartle. Pp xv, 480. £10. 1976. SBM 0 471 05464 X (Wiley)

The present status of the quasi-local mass-energy-momentum and angular momentum constructions in general relativity is reviewed. First the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities are recalled. Then the various specific constructions and their properties (both successes and defects) are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned. This review is based on the talks given at the Erwin Schrodinger Institute, Vienna, in July 1997, at the Universitat Tubingen, in May 1998, and at the National Center for Theoretical Sciences in Hsinchu and at the National Central University, Chungli, Taiwan, in July 2000.

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Quasi-Local Energy-Momentum and Angular Momentum in GR: A Review Article

The present status of the quasi-local mass, energy-momentum and angular-momentum constructions in general relativity is reviewed. First, the general ideas, concepts, and strategies, as well as the necessary tools to construct and analyze the quasi-local quantities, are recalled. Then, the various specific constructions and their properties (both successes and deficiencies are discussed. Finally, some of the (actual and potential) applications of the quasi-local concepts and specific constructions are briefly mentioned.

/pdf/quasi-local-energy-momentum-and-angular-momentum-in-general-wmf4x6598j.pdf

Quasi-Local Energy-Momentum and Angular Momentum in General Relativity.

Manifolds all of whose geodesics are closed

Presents a brief review of the theory and applications of Regge calculus in classical and quantum gravity, followed by a comprehensive bibliography which the author hopes will be of use to workers in the subject.

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Regge calculus: a brief review and bibliography

Preface. Introduction and Overview. 1. Basics of Extension and Lifting Problems. 2. Up to Homotopy is Good Enough. 3. Homotopy Group Theory. 4. Homology and Cohomology Theories. 5. Examples in Homology and Cohomology. 6. Sheaf and Spectral Theories. 7. Bundle Theory. 8. Obstruction Theory. 9. Applications. A: Algebra. B: Topology. C: Manifolds and Bundles. D: Tables of Homotopy Groups. E: Computational Algebraic Topology. Bibliography. Index.

A User’s Guide to Algebraic Topology

We find the Riemann curvature tensors of all leftinvariant Lorentzian metrics on 3-dimensional Lie groups. MSC(1991): Primary 53C50; Secondary 53B30, 53C30. −−−−−−−−−−−−−−−−−−−−−−−−−−→Υ· ∞·←−−−−−−−−−−−−−−−−−−−−−−−−−− Supported by Project XUGA8050189, Xunta de Galicia, Spain. On leave from Math. Dept., Wichita State Univ., Wichita KS 67260, U.S.A., pparker@twsuvm.uc.twsu.edu Partially supported by DGICYT-Spain.

Left-invariant lorentzian metrics on 3-dimensional lie groups

Let M be a smooth manifold with a linear connection. If M is pseudoconvex, disprisoning, and has no conjugate points, then each pair of points of M is joined by at least one geodesic.

Pseudoconvexity and geodesic connectedness

While still a semidirect product, the isometry group can be strictly larger than the obvious Riemannian analogue I. In fact, there are three relevant groups of isometries, Ispl = I = I, and Ispl < I < I is possible when the center is degenerate. When the center is nondegenerate, Ispl = I.

https://www.math.wichita.edu/~pparker/research/pRnLg/CP5.pdf

Isometry groups of pseudoriemannian 2-step nilpotent lie groups

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Phillip E. Parker

Papers

A User’s Guide to Algebraic Topology

Left-invariant lorentzian metrics on 3-dimensional lie groups

Pseudoconvexity and geodesic connectedness

Isometry groups of pseudoriemannian 2-step nilpotent lie groups

Klein-Gordon solvability and the geometry of geodesics