By Tobias H. Colding
By Torsten Wedhorn
This booklet explains thoughts which are crucial in just about all branches of contemporary geometry corresponding to algebraic geometry, advanced geometry, or non-archimedian geometry. It makes use of the main obtainable case, genuine and complicated manifolds, as a version. the writer in particular emphasizes the adaptation among neighborhood and worldwide questions. Cohomology thought of sheaves is brought and its utilization is illustrated by way of many examples.
By Oswald; Whitehead, J. H. C. Veblen
By Roman Bezrukavnikov
The booklet is dedicated to the geometrical development of the representations of Lusztig's small quantum teams at roots of cohesion. those representations are discovered as a few areas of vanishing cycles of perverse sheaves over configuration areas. As an program, the bundles of conformal blocks over the moduli areas of curves are studied. The e-book is meant for experts in workforce representations and algebraic geometry.
By Keith Burns
Available, concise, and self-contained, this e-book bargains an exceptional creation to 3 similar topics: differential geometry, differential topology, and dynamical structures. issues of unique curiosity addressed within the ebook contain Brouwer's mounted aspect theorem, Morse concept, and the geodesic flow.Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential types, and integration on manifolds give you the beginning for lots of purposes in dynamical platforms and mechanics. The authors additionally speak about the Gauss-Bonnet theorem and its implications in non-Euclidean geometry versions. The differential topology point of the ebook facilities on classical, transversality conception, Sard's theorem, intersection thought, and fixed-point theorems. the development of the de Rham cohomology builds additional arguments for the robust connection among the differential constitution and the topological constitution. It additionally furnishes the various instruments beneficial for a whole figuring out of the Morse thought. those discussions are through an creation to the speculation of hyperbolic platforms, with emphasis at the crucial function of the geodesic move. the combination of geometric conception, topological concept, and urban purposes to dynamical structures set this e-book aside. With fresh, transparent prose and powerful examples, the authors' intuitive technique creates a remedy that's understandable to relative newcomers, but rigorous sufficient for people with extra heritage and adventure within the box.
By Y.G. Oh, K. Fukaya, Y-G Oh, K. Ono, G. Tian
Complaints of the 4th KIAS Annual foreign convention, held in August 14-18, 2000, Seoul, South Korea. best specialists within the box discover the newer advancements with regards to homological replicate symmetry, Floer thought, D-branes and Gromov-Witten invariants.
By Anthony Tromba
These lecture notes are in keeping with the joint paintings of the writer and Arthur Fischer on Teichmiiller idea undertaken within the years 1980-1986. because then a lot of our colleagues have inspired us to put up our method of the topic in a concise structure, simply obtainable to a vast mathematical viewers. even if, it used to be the invitation by means of the school of the ETH Ziirich to carry the ETH N achdiplom-Vorlesungen in this fabric which supplied the chance for the writer to strengthen our examine papers right into a structure compatible for mathematicians with a modest heritage in differential geometry. We additionally was hoping it is going to give you the foundation for a graduate path stressing the appliance of basic principles in geometry. For this chance the writer needs to thank Eduard Zehnder and Jiirgen Moser, appearing director and director of the Forschungsinstitut fiir Mathematik on the ETH, Gisbert Wiistholz, chargeable for the Nachdiplom Vorlesungen and the total ETH school for his or her aid and hot hospitality. This new method of Teichmiiller concept awarded right here used to be undertaken for 2 purposes. First, it used to be transparent that the classical technique, utilizing the speculation of extremal quasi-conformal mappings (in this method we thoroughly keep away from using quasi-conformal maps) was once no longer simply appropriate to the idea of minimum surfaces, a box of curiosity of the writer over a long time. moment, many different energetic mathematicians, who at a variety of occasions wanted a few Teichmiiller idea, have came upon the classical process inaccessible to them.
By S. Hyde, Z. Blum, T. Landh, S. Lidin, B.W. Ninham, S. Andersson, K. Larsson
This booklet develops the thesis that constitution and serve as in quite a few condensed platforms - from the atomic assemblies in inorganic frameworks and natural molecules, via molecular self-assemblies to proteins - could be unified whilst curvature and floor geometry are taken including molecular form and forces. An brilliant number of man made and organic assemblies could be thoroughly modelled and understood by way of hyperbolic surfaces, whose richness and sweetness are just now being published by means of utilized mathematicians, physicists, chemists and crystallographers. those surfaces, frequently as regards to periodic minimum surfaces, weave and twist via area, carving out interconnected labyrinths whose diversity of topologies and symmetries problem the imaginitive powers.
The ebook bargains an outline of those constructions and structural alterations, convincingly demonstrating their ubiquity in covalent frameworks from zeolites used for cracking oil and toxins keep watch over to enzymes and structural proteins, thermotropic and lyotropic bicontinuous mesophases shaped via surfactants, detergents and lipids, man made block copolymer and protein networks, in addition to organic cellphone assemblies, from muscular tissues to membranes in prokaryotic and eukaryotic cells. The relation among constitution and serve as is analysed by way of the formerly overlooked
hidden variables of curvature and topology. therefore, the catalytic job of zeolites and enzymes, some of the best fabric houses of interpenetrating networks in microstructured polymer composites, the shipping necessities in cells, the transmission of nerve signs and the folding of DNA will be extra simply understood within the mild of this.
The textual content is liberally sprinkled with figures and color plates, making it available to either the start graduate pupil and researchers in condensed subject physics and chemistry, mineralogists, crystallographers and biologists.
By Luther Pfahler Eisenhart
A few of the earliest books, quite these relationship again to the 1900s and sooner than, are actually tremendous scarce and more and more dear. we're republishing those vintage works in reasonable, prime quality, sleek versions, utilizing the unique textual content and paintings.
By Helmut Eschrig
A concise yet self-contained advent of the vital techniques of recent topology and differential geometry on a mathematical point is given particularly with functions in physics in brain. All uncomplicated ideas are systematically supplied together with sketches of the proofs of such a lot statements. tender finite-dimensional manifolds, tensor and external calculus working on them, homotopy, (co)homology concept together with Morse conception of severe issues, in addition to the speculation of fiber bundles and Riemannian geometry, are handled. Examples from physics include topological fees, the topology of periodic boundary stipulations for solids, gauge fields, geometric levels in quantum physics and gravitation.