Category: Topology

By Wolfgang Lück

Dies ist ein neues und modernes Lehrbuch über Topologie. Hauptgegenstand des Buches sind Homologie-, Kohomologietheorien und Mannigfaltigkeiten. Die ersten acht Kapitel geben eine Einführung in die "Algebraische Topologie": es werden Begriffe wie Homologie, CW-Komplexe, Produkte und Poincare Dualitäte eingeführt und deren Anwendungen diskutiert. In den davon unabhängigen Kapiteln nine bis thirteen werden Differentialformen und der Satz von Stokes auf Mannigfaltigkeiten behandelt. Diese Kapitel sind geeignet für eine Vorlesung "Analysis III" oder "Analysis auf Mannigfaltigkeiten". Die in den letzten beiden Kapiteln behandelte de Rham Kohomologie und der Satz von de Rham verbinden diese beiden Teile. Die Darstellung ist komprimiert und kommt schnell auf das Wesentliche, das Buch ist vielseitig in der Lehre einsetzbar.

By Peter May

Because it used to be first released in 1967, Simplicial gadgets in Algebraic Topology has been the normal reference for the speculation of simplicial units and their dating to the homotopy concept of topological areas. J. Peter may possibly provides a lucid account of the elemental homotopy concept of simplicial units (discrete analogs of topological areas) that have performed a principal function in algebraic topology ever considering the fact that their advent within the overdue Forties.

By V. V. Prasolov

This publication is an advent to easy topology offered in an intuitive method, emphasizing the visible point. Examples of nontrivial and sometimes unforeseen topological phenomena acquaint the reader with the picturesque global of knots, hyperlinks, vector fields, and two-dimensional surfaces. The ebook starts with definitions offered in a tangible and perceptible means, on a regular point, and steadily makes them extra distinct and rigorous, ultimately attaining the extent of quite refined proofs. this enables significant difficulties to be tackled from the outset. one other strange trait of this publication is that it offers normally with buildings and maps, instead of with proofs that convinced maps and buildings do or don't exist. the various illustrations are an important function. The ebook is on the market not just to undergraduates but in addition to highschool scholars and may curiosity any reader who has a few feeling for the visible attractiveness of geometry and topology.

By John McCleary

Spectral sequences are one of the so much stylish and robust tools of computation in arithmetic. This publication describes probably the most very important examples of spectral sequences and a few in their so much astonishing purposes. the 1st half treats the algebraic foundations for this type of homological algebra, ranging from casual calculations. the center of the textual content is an exposition of the classical examples from homotopy concept, with chapters at the Leray-Serre spectral series, the Eilenberg-Moore spectral series, the Adams spectral series, and, during this re-creation, the Bockstein spectral series. The final a part of the publication treats purposes all through arithmetic, together with the speculation of knots and hyperlinks, algebraic geometry, differential geometry and algebra. this is often a superb reference for college students and researchers in geometry, topology, and algebra.

By Alexander Arhangel'skii, Mikhail Tkachenko

This booklet provides a large number of fabric, either vintage and up to date (on get together, unpublished) in regards to the kinfolk of Algebra and Topology. It consequently belongs to the realm known as Topological Algebra. extra in particular, the items of the research are sophisticated and infrequently unforeseen phenomena that ensue whilst the continuity meets and correctly feeds an algebraic operation. one of these mix offers upward thrust to many vintage buildings, together with topological teams and semigroups, paratopological teams, and so on. designated emphasis is given to tracing the effect of compactness and its generalizations at the houses of an algebraic operation, inflicting from time to time the automated continuity of the operation. the most scope of the e-book, although, is outdoors of the in the community compact constructions, therefore distinguishing the monograph from a sequence of extra conventional textbooks.

The booklet is exclusive in that it offers vitally important fabric, dispersed in 1000's of analysis articles, no longer coated by means of any monograph in lifestyles. The reader is lightly brought to an awesome global on the interface of Algebra, Topology, and Set concept. He/she will locate that how to the frontier of the data is sort of brief -- virtually each part of the e-book comprises numerous exciting open difficulties whose ideas can give a contribution considerably to the realm.

Contents: advent to Topological teams and Semigroups; correct Topological and Semitopological teams; Topological teams: easy structures; a few designated periods of Topological teams; Cardinal Invariants of Topological teams; Moscow Topological teams and Completions of teams; unfastened Topological teams; R-Factorizable Topological teams; Compactness and its Generalizations in Topological teams; activities of Topological teams on Topological Spaces.

By Filippo Callegaro, Frederick Cohen, Corrado De Concini, Eva Maria Feichtner, Giovanni Gaiffi, Mario Salvetti

This ebook collects the clinical contributions of a gaggle of prime specialists who took half within the INdAM assembly held in Cortona in September 2014. With combinatorial ideas because the important topic, it specializes in fresh advancements in configuration areas from quite a few views. It additionally discusses their functions in parts starting from illustration conception, toric geometry and geometric team idea to utilized algebraic topology.

By Michael I. Monastyrsky

This considerably extended moment version of Riemann, Topology, and Physics combines a desirable account of the existence and paintings of Bernhard Riemann with a lucid dialogue of present interplay among topology and physics, the writer, a exclusive mathematical physicist, takes into consideration his personal study on the Riemann records of Göttingen collage and advancements during the last decade that attach Riemann with a variety of major principles and techniques mirrored all through modern arithmetic and physics.

Special realization is paid partially one to effects at the Riemann–Hilbert challenge and, partially , to discoveries in box idea and condensed subject equivalent to the quantum corridor impression, quasicrystals, membranes with nontrivial topology, "fake" differential buildings on four-dimensional Euclidean area, new invariants of knots and extra. In his really brief lifetime, this nice mathematician made remarkable contributions to almost all branches of arithmetic; this day Riemann’s identify looks prominently during the literature.

"The e-book is extremely recommendable—for scholars and medical workers—not just for the precious info in it, but in addition for its spirit: heritage and better arithmetic should not dry right here; they turn into alive and encourage additional studies."—ZAA

"This is a brand new translation of a booklet first released in English in 1987... Translated from Russian...it comprises separate yet comparable works. the 1st is an account of the lifestyles and paintings of Riemann, the second one an account of a number of varied subject matters in physics that are illuminated through the advent of topological principles. The dialogue of Riemann is even higher within the re-creation. The mathematical account is richer and numerous blunders were corrected... the second one part has been revised in an identical fashion... It has additionally been enriched by way of a brand new bankruptcy which starts off with von Neumann algebras and the paintings of Vaughn Jones... The publication does 3 issues rather well: it reminds us of the variety and intensity of Riemann’s pursuits, that are emblematic of what the writer values in mathematical physics; describes the various many successes of Russian mathematicians and physicists; and it presents a lucid account of a few smooth paintings during which topology is certainly utilized. Books like this are important for the healthiness of arithmetic and it's to be was hoping that extra may be written."---Mathematical Reviews

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By Masaki Kashiwara

By Weiping Li, Loretta Bartolini, Jesse Johnson, Feng Luo, Robert Myers

By Erica Flapan

During this excellent topology textual content, the readers not just know about knot idea, three-d manifolds, and the topology of embedded graphs, but additionally their function in knowing molecular constructions. such a lot effects defined within the textual content are stimulated by way of the questions of chemists or molecular biologists, notwithstanding they generally transcend answering the unique query requested. No particular mathematical or chemical must haves are required. The textual content is more suitable by way of approximately 2 hundred illustrations and a hundred routines. With this attention-grabbing booklet, undergraduate arithmetic scholars break out the realm of natural summary idea and input that of actual molecules, whereas chemists and biologists locate basic and transparent yet rigorous definitions of mathematical suggestions they deal with intuitively of their paintings.