Category: Topology

By Vladislav V Goldberg, Shiing-Shen Chern

Foreword through S S Chern
In 1926-27, Cartan gave a chain of lectures within which he brought external types on the very starting and used greatly orthogonal frames all through to enquire the geometry of Riemannian manifolds. during this path he solved a chain of difficulties in Euclidean and non-Euclidean areas, in addition to a sequence of variational difficulties on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of those Cartan's lectures and released them as a booklet entitled Riemannian Geometry in an Orthogonal body. This ebook has many inventions, akin to the concept of intrinsic common differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional area or in an area of continuous curvature, an affine connection outlined in a typical fiber package deal of a submanifold, and so forth. It has now been translated into English via Vladislav V Goldberg, presently unique Professor of arithmetic on the New Jersey Institute of expertise, united states, who additionally edited the Russian version.

By International Conference on Algebraic Topology, Paul Gregory Goerss, Stewart Priddy

As a part of its sequence of ""Emphasis Years in Mathematics"", Northwestern college hosted a global convention on Algebraic Topology. the aim of the convention was once to boost new connections among homotopy thought and different components of arithmetic. This complaints quantity grew out of that occasion. issues mentioned comprise algebraic geometry, cohomology of teams, algebraic $K$-theory, and $\mathbb{A}^1$ homotopy idea. one of the individuals to the quantity have been Alejandro Adem, Ralph L. Cohen, Jean-Louis Loday, and so on. The booklet is appropriate for graduate scholars and examine mathematicians attracted to homotopy thought and its courting to different components of arithmetic

By Ali Reza Ashrafi, Modjtaba Ghorbani (auth.), Franco Cataldo, Ante Graovac, Ottorino Ori (eds.)

Mathematics and Topology of Fullerenes offers a accomplished review of clinical and technical thoughts in theoretical and experimental stories. subject matters integrated during this multi-author quantity contain: Clar constructions for conjugated nanostructures; counting polynomials of fullerenes; topological indices of fullerenes; the wiener index of nanotubes; toroidal fullerenes and nanostars; C60 Structural relations: a topological examine; neighborhood combinatorial characterization of fullerenes; computation of chosen topological indices of C60 and C80 Fullerenes through the distance software; 4valent- analogues of fullerenes; a close atlas of Kekule buildings of C60.

This multi-author quantity is concentrated at complicated graduates and researchers operating in carbon fabrics, chemistry and physics.

By Togo Nishiura

Absolute measurable house and absolute null area are very outdated topological notions, constructed from recognized evidence of descriptive set thought, topology, Borel degree thought and research. This monograph systematically develops and returns to the topological and geometrical origins of those notions. Motivating the improvement of the exposition are the motion of the gang of homeomorphisms of an area on Borel measures, the Oxtoby-Ulam theorem on Lebesgue-like measures at the unit dice, and the extensions of this theorem to many different topological areas. lifestyles of uncountable absolute null area, extension of the Purves theorem and up to date advances on homeomorphic Borel likelihood measures at the Cantor house, are one of the issues mentioned. A short dialogue of set-theoretic effects on absolute null area is given, and a four-part appendix aids the reader with topological measurement idea, Hausdorff degree and Hausdorff measurement, and geometric degree thought.

By Alexander Kechris, Benjamin D. Miller

This quantity presents a self-contained creation to a few issues in orbit equivalence concept, a department of ergodic concept. the 1st chapters specialise in hyperfiniteness and amenability. incorporated listed below are proofs of Dye's theorem that chance measure-preserving, ergodic activities of the integers are orbit identical and of the concept of Connes-Feldman-Weiss deciding on amenability and hyperfiniteness for non-singular equivalence family members. The presentation here's frequently encouraged through descriptive set thought, and Borel and customary analogs of assorted effects are mentioned. the ultimate bankruptcy is a close account of Gaboriau's contemporary effects at the concept of prices for equivalence kinfolk and teams and its purposes to proving pressure theorems for activities of loose groups.

By Alexander Arhangel'skii, Mikhail Tkachenko

This publication provides a large number of fabric, either vintage and up to date (on party, unpublished) concerning the relatives of Algebra and Topology. It hence belongs to the realm known as Topological Algebra. extra particularly, the gadgets of the examine are refined and infrequently unforeseen phenomena that take place while the continuity meets and correctly feeds an algebraic operation. one of these blend offers upward push to many vintage constructions, together with topological teams and semigroups, paratopological teams, and so on. specified emphasis is given to tracing the impact of compactness and its generalizations at the houses of an algebraic operation, inflicting every so often the automated continuity of the operation. the most scope of the publication, although, is outdoors of the in the neighborhood compact buildings, hence distinguishing the monograph from a chain of extra conventional textbooks.

The publication is exclusive in that it offers vitally important fabric, dispersed in 1000s of study articles, no longer lined by means of any monograph in lifestyles. The reader is lightly brought to an grand global on the interface of Algebra, Topology, and Set idea. He/she will locate that the right way to the frontier of the data is kind of brief -- nearly each element of the publication comprises numerous fascinating open difficulties whose recommendations can give a contribution considerably to the world.

Contents: advent to Topological teams and Semigroups; correct Topological and Semitopological teams; Topological teams: simple structures; a few precise 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 Wolfgang Luck, Shmuel Weinberger, Michael Farber

This quantity offers the lawsuits of the Tel Aviv overseas Topology convention held throughout the distinctive Topology software at Tel Aviv collage. The e-book is devoted to Professor Mel Rothenberg at the get together of his sixty fifth birthday. His contributions to topology are renowned - from the early paintings on triangulations to various papers on transformation teams and on geometric and analytic elements of torsion thought. present study regarding these contributions are suggested during this booklet. insurance is incorporated at the following themes: vanishing theorems for the Dirac operator, the speculation of Reidemeister torsion (including limitless dimensional flat bundles), Nobikov-Shubin invariants of manifolds, topology of workforce activities, Lusternik-Schnirelman thought for closed 1-forms, finite style invariants of hyperlinks and 3-manifolds, equivariant cobordisms, equivariant orientations and Thom isomorphisms, and extra

By Hans Freudenthal

L. E. J. Brouwer gathered Works, quantity 2: Geometry, research, Topology, and Mechanics specializes in the contributions and ideas of Brouwer on geometry, topology, research, and mechanics, together with non-Euclidean areas, integrals, and surfaces.

The e-book first ponders on non-Euclidean areas and quintessential theorems, lie teams, and aircraft transition theorem. Discussions specialize in comments on a number of integrals, strength box of the non-Euclidean areas with damaging curvature, distinction quotients and differential quotients, characterization of the Euclidean and non-Euclidean movement teams, and non-stop one-one modifications of surfaces in themselves. The ebook additionally takes a glance at vector fields on surfaces and new tools in topology, together with non-stop vector distributions on surfaces and orthogonal trajectories of the orbits of a one parameter aircraft projective team. The e-book then ponders on mechanics and topology of surfaces, in addition to the movement of a particle at the backside of a rotating vessel below the impression of gravitational strength.

The book is a useful reference for researchers attracted to geometry, topology, research, and mechanics.

By S. Kojima, M. Seppala, Y. Matsumoto, K. Saito

This lawsuits is a suite of articles on Topology and Teichmuller areas. distinctive emphasis is being wear the common Teichmuller area, the topology of moduli of algebraic curves, the distance of representations of discrete teams, Kleinian teams and Dehn filling deformations, the geometry of Riemann surfaces, and a few similar issues.

By Jorge Picado

Until the mid-twentieth century, topological reports have been all in favour of the speculation of compatible constructions on units of issues. the concept that of open set exploited because the twenties provided an expression of the geometric instinct of a "realistic" position (spot, grain) of non-trivial extent.

Imitating the behaviour of open units and their kinfolk ended in a brand new method of topology flourishing because the finish of the fifties.It has proved to be priceless in lots of respects. Neglecting issues, purely little details used to be misplaced, whereas deeper insights were won; in addition, many effects formerly depending on selection ideas grew to become optimistic. the result's usually a smoother, instead of a extra entangled, theory.

No monograph of this nature has seemed considering Johnstone's celebrated Stone Spaces in 1983. the current publication is meant as a bridge from that point to the current. lots of the fabric looks the following in booklet shape for the 1st time or is gifted from new issues of view. appendices offer an advent to a few needful suggestions from order and type theories.