Topology

By Robert F. Brown

This 3rd version is addressed to the mathematician or graduate pupil of arithmetic - or perhaps the well-prepared undergraduate - who would favor, with at least heritage and guidance, to appreciate the various appealing effects on the middle of nonlinear research. in accordance with carefully-expounded rules from a number of branches of topology, and illustrated by way of a wealth of figures that attest to the geometric nature of the exposition, the ebook can be of sizeable assist in supplying its readers with an knowing of the math of the nonlinear phenomena that symbolize our actual international. integrated during this re-creation are numerous new chapters that current the fastened aspect index and its functions. The exposition and mathematical content material is greater all through. This ebook is perfect for self-study for mathematicians and scholars attracted to such components of geometric and algebraic topology, practical research, differential equations, and utilized arithmetic. it's a sharply targeted and hugely readable view of nonlinear research through a working towards topologist who has visible a transparent route to figuring out. "For the topology-minded reader, the publication certainly has much to supply: written in a truly own, eloquent and instructive sort it makes one of many highlights of nonlinear research obtainable to a large audience."-Monatshefte fur Mathematik (2006)

By A. Marden

We are living in a 3-dimensional area; what kind of area is it? will we construct it from easy geometric items? The solutions to such questions were present in the final 30 years, and Outer Circles describes the elemental arithmetic wanted for these solutions in addition to making transparent the grand layout of the topic of hyperbolic manifolds as an entire. the aim of Outer Circles is to supply an account of the modern thought, obtainable to these with minimum formal history in topology, hyperbolic geometry, and intricate research. The textual content explains what's wanted, and gives the services to exploit the first instruments to reach at an intensive knowing of the large photo. This photo is extra crammed out through a number of workouts and expositions on the ends of the chapters and is complemented via a great quantity of top quality illustrations. there's an intensive bibliography for extra learn.

By Megumi Harada, Yael Karshon, Mikiya Masuda, Taras Panov

Toric topology is the research of algebraic, differential, symplectic-geometric, combinatorial, and homotopy-theoretic points of a selected category of torus activities whose quotients are hugely established. The combinatorial homes of this quotient and the equivariant topology of the unique manifold engage in a wealthy number of methods, therefore illuminating sophisticated points of either the combinatorics and the equivariant topology. a number of the motivations and guiding rules of the sector are supplied via (though no longer restricted to) the speculation of toric kinds in algebraic geometry in addition to that of symplectic toric manifolds in symplectic geometry. This quantity is the court cases of the overseas convention on Toric Topology held in Osaka in May-June 2006. It includes approximately 25 learn and survey articles written through convention audio system, overlaying many various points of, and techniques to, torus activities, reminiscent of these pointed out above.Some of the manuscripts are survey articles, meant to provide a wide assessment of a side of the topic; all manuscripts consciously objective to be available to a huge analyzing viewers of scholars and researchers drawn to the interplay of the themes concerned. we are hoping that this quantity serves as an attractive invitation to this rising box

By Maurice Frechet, Ky Fan, Howard W. Eves

An easy textual content that may be understood through someone with a history in highschool geometry, Invitation to Combinatorial Topology deals a stimulating initiation to big topological principles. This translation from the unique French does complete justice to the text's coherent presentation in addition to to its wealthy historic content material. matters contain the issues inherent to coloring maps, homeomorphism, purposes of Descartes' theorem, and topological polygons. issues of the topological category of closed surfaces conceal uncomplicated operations, use of ordinary kinds of polyhedra, aid to general shape, and alertness to the geometric thought of features. 1967 ed. 108 Figures. Bibliography. Index.

By S. K. Donaldson, C. B. Thomas

Those volumes are according to lecture classes and seminars given on the LMS Durham Symposium at the geometry of low-dimensional manifolds. This zone has been certainly one of extreme study lately, with significant breakthroughs that experience illuminated the way in which a few diverse topics (topology, differential and algebraic geometry and mathematical physics) have interaction.

By Yann Ollivier, Hervé Pajot, Cedric Villani

The idea of optimum transportation has its origins within the eighteenth century whilst the matter of transporting assets at a minimum expense used to be first formalised. via next advancements, rather in contemporary a long time, it has develop into a robust glossy thought. This e-book includes the complaints of the summer time tuition 'Optimal Transportation: concept and purposes' held on the Fourier Institute in Grenoble. the development introduced jointly mathematicians from natural and utilized arithmetic, astrophysics, economics and machine technological know-how. half I of this ebook is dedicated to introductory lecture notes available to graduate scholars, whereas half II comprises examine papers. jointly, they signify a helpful source on either basic and complex points of optimum transportation, its functions, and its interactions with research, geometry, PDE and chance, city making plans and economics. themes coated comprise Ricci movement, the Euler equations, practical inequalities, curvature-dimension stipulations, and traffic jam.

By Ulrich Koschorke

By Rob Sturman, Julio M. Ottino, Stephen Wiggins

Blending procedures take place in lots of technological and average functions, with size and time scales starting from the very small to the very huge. the range of difficulties may give upward thrust to a range of methods. Are there suggestions which are primary to them all? Are there instruments that permit for prediction and quantification? The authors express how a number of flows in very varied settings own the attribute of streamline crossing. This thought could be put on company mathematical footing through associated Twist Maps (LTMs), that is the relevant organizing precept of this publication. The authors speak about the definition and development of LTMs, supply examples of particular mixers that may be analyzed within the LTM framework and introduce a couple of mathematical concepts that are then dropped at endure at the challenge of fluid blending. In a last bankruptcy, they current a few open difficulties and new instructions.

By Jeffrey R. Weeks

Retaining the traditional of excellence set via the former version, this textbook covers the fundamental geometry of 2- and three-d areas Written by means of a grasp expositor, top researcher within the box, and MacArthur Fellow, it contains experiments to figure out the real form of the universe and comprises illustrated examples and fascinating routines that educate mind-expanding rules in an intuitive and casual manner. Bridging the distance from geometry to the most recent paintings in observational cosmology, the publication illustrates the relationship among geometry and the habit of the actual universe and explains how radiation last from the large bang may perhaps show the particular form of the universe.

By M.M. Cohen

This publication grew out of classes which I taught at Cornell collage and the collage of Warwick in the course of 1969 and 1970. I wrote it due to a robust trust that there might be on hand a semi-historical and geo­ metrically prompted exposition of J. H. C. Whitehead's attractive thought of simple-homotopy kinds; that tips to comprehend this thought is to grasp how and why it used to be equipped. This trust is buttressed through the truth that the main makes use of of, and advances in, the idea in contemporary times-for instance, the s-cobordism theorem (discussed in §25), using the idea in surgical procedure, its extension to non-compact complexes (discussed on the finish of §6) and the evidence of topological invariance (given within the Appendix)-have come from simply such an figuring out. A moment cause of writing the publication is pedagogical. this can be a very good topic for a topology pupil to "grow up" on. The interaction among geometry and algebra in topology, every one enriching the opposite, is superbly illustrated in simple-homotopy concept. the topic is available (as within the classes pointed out on the outset) to scholars who've had an outstanding one­ semester path in algebraic topology. i've got attempted to write down proofs which meet the wishes of such scholars. (When an evidence was once passed over and left as an workout, it was once performed with the welfare of the coed in brain. He should still do such workouts zealously.