Download E-books Morse Theory and Floer Homology (Universitext) PDF

By Michèle Audin, Mihai Damian

This publication is an creation to fashionable tools of symplectic topology. it's dedicated to explaining the answer of an incredible challenge originating from classical mechanics: the 'Arnold conjecture', which asserts that the variety of 1-periodic trajectories of a non-degenerate Hamiltonian approach is bounded less than by way of the size of the homology of the underlying manifold.

The first half is a radical advent to Morse idea, a basic software of differential topology. It defines the Morse complicated and the Morse homology, and develops a few of their applications.

Morse homology additionally serves an easy version for Floer homology, that's lined within the moment half. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been the most important within the fresh achievements in symplectic geometry and specifically within the facts of the Arnold conjecture. The development blocks of Floer homology are extra elaborate and indicate using extra subtle analytical equipment, all of that are defined during this moment part.

The 3 appendices current a couple of must haves in differential geometry, algebraic topology and analysis.

The publication originated in a graduate path given at Strasbourg college, and encompasses a huge diversity of figures and workouts. Morse conception and Floer Homology could be fairly worthwhile for graduate and postgraduate students.

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Download E-books Some Nonlinear Problems in Riemannian Geometry (Springer Monographs in Mathematics) PDF

By Thierry Aubin

This ebook offers with such vital matters as variational tools, the continuity approach, parabolic equations on fiber bundles, principles referring to issues of focus, blowing-up method, geometric and topological equipment. It explores vital geometric difficulties which are of curiosity to many mathematicians and scientists yet have only in the near past been partly solved.

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Download E-books An Introduction to the Kähler-Ricci Flow (Lecture Notes in Mathematics) PDF

This quantity collects lecture notes from classes provided at numerous meetings and workshops, and gives the 1st exposition in booklet kind of the fundamental concept of the Kähler-Ricci move and its present state of the art. whereas numerous very good books on Kähler-Einstein geometry can be found, there were no such works at the Kähler-Ricci stream. The publication will function a worthwhile source for graduate scholars and researchers in complicated differential geometry, advanced algebraic geometry and Riemannian geometry, and may optimistically foster extra advancements during this attention-grabbing sector of research.
 
The Ricci move used to be first brought by way of R. Hamilton within the early Eighties, and is valuable in G. Perelman’s celebrated facts of the Poincaré conjecture. whilst really expert for Kähler manifolds, it turns into the Kähler-Ricci circulate, and decreases to a scalar PDE (parabolic advanced Monge-Ampère equation).
As a spin-off of his leap forward, G. Perelman proved the convergence of the Kähler-Ricci circulate on Kähler-Einstein manifolds of optimistic scalar curvature (Fano manifolds). presently after, G. Tian and J. tune found a fancy analogue of Perelman’s principles: the Kähler-Ricci movement is a metric embodiment of the minimum version application of the underlying manifold, and flips and divisorial contractions think the position of Perelman’s surgeries.

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Download E-books Integral Geometry of Tensor Fields (Inverse and Ill-Posed Problems) PDF

Crucial geometry could be outlined as settling on a few functionality or a extra normal volume, that is outlined on a manifold, given its integrals over submanifolds or a prescribed classification. during this publication, purely critical geometry difficulties are thought of for which the submanifolds are one-dimensional. The e-book bargains with crucial geometry of symmetric tensor fields. This part of fundamental geometry will be regarded as the mathematical foundation for tomography or anisotropic media whose interplay with sounding radiation relies basically at the path during which the latter propagates. the most mathematical items tackled were supply the time period "ray transform", which refers mostly to optical and seismic rays instead of to X-rays. This publication might be of curiosity to mathematicians, engineers, desktop scientists and physicists who're woking within the fields of light-conductor know-how, plasma physics tomography and liquid crystals.

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Download E-books Symplectic Geometry: An Introduction based on the Seminar in Bern, 1992 (Progress in Mathematics) PDF

By B. Aebischer, M. Borer

The seminar Symplectic Geometry on the college of Berne in summer time 1992 confirmed that the subject of this booklet is a really energetic box, the place many alternative branches of arithmetic come tog9ther: differential geometry, topology, partial differential equations, variational calculus, and complicated research. As traditional in this kind of state of affairs, it can be tedious to assemble all of the useful parts. the current ebook is meant to provide the nonspecialist a superb advent to the new advancements in symplectic and get in touch with geometry. bankruptcy 1 offers a evaluation of the symplectic crew Sp(n,R), sympkctic manifolds, and Hamiltonian platforms (last yet no longer least to mend the notations). The 1\Iaslov index for closed curves in addition to arcs in Sp(n, R) is mentioned. This index should be utilized in chapters five and eight. bankruptcy 2 incorporates a extra distinctive account of symplectic manifolds commence­ ing with an evidence of the Darboux theorem asserting that there aren't any neighborhood in­ variations in symplectic geometry. an important examples of symplectic manifolds should be brought: cotangent areas and Kahler manifolds. ultimately we talk about the idea of coadjoint orbits and the Kostant-Souriau theorem, that are involved in the query of which homogeneous areas hold a symplectic constitution.

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Download E-books Introduction to Hyperbolic Geometry (Universitext) PDF

By Arlan Ramsay

This e-book is an advent to hyperbolic and differential geometry that gives fabric within the early chapters which may function a textbook for the standard higher department path on hyperbolic geometry. For that fabric, the scholars have to be accustomed to calculus and linear algebra and keen to simply accept one complicated theorem from research with out evidence. The booklet is going way past the traditional direction in later chapters, and there's adequate fabric for an honors path, or for supplementary examining. certainly, components of the publication were used for either varieties of classes. Even a few of what's within the early chapters could absolutely no longer be nec­ essary for the standard path. for instance, distinctive proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly­ gons into triangles, those proofs are integrated for the sake of completeness, however the effects themselves are so plausible that the majority scholars may still bypass the proofs on a primary studying. The axioms used are sleek in personality and extra "user pleasant" than the normal ones. The accepted actual quantity method is used as an in­ gredient instead of showing as a result axioms. even though, it's going to no longer be concept that the geometric remedy is when it comes to types: this is often an axiomatic method that's simply less demanding than the normal ones.

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Download E-books Noncompact Problems at the Intersection of Geometry, Analysis, and Topology: Proceedings of the Brezis-Browder Conference, Noncompact Variational ... Rutgers, the State (Contemporary Mathematics) PDF

This court cases quantity comprises articles from the convention held at Rutgers collage in honor of Haim Brezis and Felix Browder, mathematicians who've had a profound effect on partial differential equations, sensible research, and geometry. Mathematicians attending the convention had pursuits in noncompact variational difficulties, pseudo-holomorphic curves, singular and tender recommendations to difficulties admitting a conformal (or a few team) invariance, Sobolev areas on manifolds, and configuration areas. someday of the development was once dedicated to Einstein equations and comparable issues. the fabric is acceptable for graduate scholars and researchers attracted to difficulties in research and differential equations on noncompact manifolds.

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Download E-books Lectures on Minimal Surfaces: Volume 1, Introduction, Fundamentals, Geometry and Basic Boundary Value Problems PDF

By Johannes C. C. Nitsche

This 1989 monograph offers with parametric minimum surfaces in Euclidean area. the writer provides a extensive survey which extends from the classical beginnings to the present scenario while highlighting a number of the subject's major gains and interspersing the mathematical improvement with pertinent historic feedback. The presentation is whole and is complemented by means of a bibliography of approximately 1600 references. The cautious expository sort and emphasis on geometric features are super useful. additionally, within the years top as much as the ebook of this ebook, the speculation of minimum surfaces was once discovering expanding program to different parts of arithmetic and the actual sciences making sure that this account will attract non-specialists in addition.

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Download E-books An Introduction to Manifolds (Universitext) PDF

By Loring W. Tu

Manifolds, the higher-dimensional analogs of soft curves and surfaces, are primary items in sleek arithmetic. Combining facets of algebra, topology, and research, manifolds have additionally been utilized to classical mechanics, common relativity, and quantum box idea. during this streamlined advent to the topic, the speculation of manifolds is gifted with the purpose of aiding the reader in attaining a quick mastery of the fundamental subject matters. through the top of the ebook the reader may be capable of compute, at the least for easy areas, essentially the most uncomplicated topological invariants of a manifold, its de Rham cohomology. alongside the way in which, the reader acquires the data and abilities beneficial for extra examine of geometry and topology. The needful point-set topology is integrated in an appendix of twenty pages; different appendices assessment evidence from genuine research and linear algebra. tricks and options are supplied to some of the routines and difficulties. This paintings can be utilized because the textual content for a one-semester graduate or complicated undergraduate path, in addition to through scholars engaged in self-study. Requiring in basic terms minimum undergraduate must haves, 'Introduction to Manifolds' is usually a good origin for Springer's GTM eighty two, 'Differential kinds in Algebraic Topology'.

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