Brashura Differential Geometry: Bundles, Connections, Metrics and Curvature — Clifford Taubes — Google Books This book will supply a graduate student in mathematics or theoretical physics with the fundamentals of these objects. Account Options Sign in. The Riemann curvature tensor Maps and vector bundles 6. Selected pages Title Page. Every geometer should read it, it will blow your mind, and it clifforv change your life. Nonequilibrium Statistical Physics Noelle Pottier.

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Related Research Articles A topological quantum field theory is a quantum field theory which computes topological invariants. In mathematics, specifically in topology and geometry, a pseudoholomorphic curve is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy—Riemann equation. Introduced in by Mikhail Gromov, pseudoholomorphic curves have since revolutionized the study of symplectic manifolds. In particular, they lead to the Gromov—Witten invariants and Floer homology, and play a prominent role in string theory.

In mathematics, specifically in symplectic topology and algebraic geometry, Gromov—Witten GW invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic manifold. The GW invariants may be packaged as a homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish symplectic manifolds that were previously indistinguishable.

They also play a crucial role in closed type IIA string theory. They are named after Mikhail Gromov and Edward Witten. In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology.

Floer homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology.

Andreas Floer introduced the first version of Floer homology, now called Lagrangian Floer homology, in his proof of the Arnold conjecture in symplectic geometry.

Floer also developed a closely related theory for Lagrangian submanifolds of a symplectic manifold. A third construction, also due to Floer, associates homology groups to closed three-dimensional manifolds using the Yang—Mills functional. These constructions and their descendants play a fundamental role in current investigations into the topology of symplectic and contact manifolds as well as smooth three- and four-dimensional manifolds.

In mathematics, the Gromov invariant of Clifford Taubes counts embedded pseudoholomorphic curves in a symplectic 4-manifold, where the curves are holomorphic with respect to an auxiliary compatible almost complex structure.

Ciprian Manolescu is a Romanian-American mathematician, working in gauge theory, symplectic geometry, and low-dimensional topology. Peter Benedict Kronheimer is a British mathematician, known for his work on gauge theory and its applications to 3- and 4-dimensional topology. In mathematics, a smooth algebraic curve in the complex projective plane, of degree , has genus given by the genus—degree formula In mathematics, the Weinstein conjecture refers to a general existence problem for periodic orbits of Hamiltonian or Reeb vector flows.

More specifically, the conjecture claims that on a compact contact manifold, its Reeb vector field should carry at least one periodic orbit. Tian Gang is a Chinese mathematician. He is known for his contributions to geometric analysis and quantum cohomology especially Gromov-Witten invariants, among other fields. Donaldson theory is the study of the topology of smooth 4-manifolds using moduli spaces of anti-self-dual instantons.

Important consequences of this theorem include the existence of an Exotic R4 and the failure of the smooth h-cobordism theorem in 4 dimensions. The results of Donaldson theory depend therefore on the manifold having a differential structure, and are largely false for topological 4-manifolds. John Willard Morgan is an American mathematician, with contributions to topology and geometry.

The Geometry Festival is an annual mathematics conference held in the United States. Tomasz Mrowka is an American mathematician specializing in differential geometry and gauge theory. Kefeng Liu, is a Chinese-American mathematician who is known for his contributions to geometric analysis, particularly the geometry, topology and analysis of moduli spaces of Riemann surfaces and Calabi-Yau manifolds. National Academy of Sciences "for excellence of research in the mathematical sciences published within the past ten years.

Michael Lounsbery Hutchings is an American mathematician, a professor of mathematics at the University of California, Berkeley. He is known for proving the double bubble conjecture on the shape of two-chambered soap bubbles, and for his work on circle-valued Morse theory and on embedded contact homology, which he defined.

Kenji Fukaya is a Japanese mathematician known for his work in symplectic geometry and Riemannian geometry. His many fundamental contributions to mathematics include the discovery of the Fukaya category. He is a permanent faculty member at the Simons Center for Geometry and Physics and a professor of mathematics at Stony Brook University.

Ronald Alan Fintushel is an American mathematician, specializing in low-dimensional geometric topology and the mathematics of gauge theory. Notices of the American Mathematical Society. March Bielefeld Extra Vol.

ICM Berlin, , vol. National Academy of Sciences. Archived from the original on 29 December Retrieved 13 February

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