Category «Differential Geometry»

Download Loop Spaces, Characteristic Classes and Geometric by Jean-Luc Brylinski PDF

By Jean-Luc Brylinski

This booklet offers with the differential geometry of manifolds, loop areas, line bundles and groupoids, and the family of this geometry to mathematical physics.

Various advancements in mathematical physics (e.g., in knot concept, gauge thought, and topological quantum box idea) have led mathematicians and physicists to go looking for brand new geometric buildings on manifolds and to hunt a synthesis of principles from geometry, topology and type conception. during this spirit, this publication develops the differential geometry linked to the topology and obstruction concept of convinced fiber bundles (more accurately, linked to grebes). the idea is a three-dimensional analog of the widespread Kostant--Weil conception of line bundles. specifically the curvature now turns into a 3-form.

Applications provided within the booklet contain anomaly line bundles on loop areas and anomaly functionals, crucial extensions of loop teams, Kähler geometry of the gap of knots, Cheeger--Chern--Simons secondary features sessions, and team cohomology. eventually, the final bankruptcy offers with the Dirac monopole and Dirac’s quantization of charge.

The booklet might be of curiosity to topologists, geometers, Lie theorists and mathematical physicists, in addition to to operator algebraists. it's written for graduate scholars and researchers, and may be an exceptional textbook. It has a self-contained advent to the speculation of sheaves and their cohomology, line bundles and geometric prequantization à l. a. Kostant--Souriau.

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Download Geometry and analysis on manifolds : in memory of professor by Takushiro Ochiai, Toshiki Mabuchi, Yoshiaki Maeda, Junjiro PDF

By Takushiro Ochiai, Toshiki Mabuchi, Yoshiaki Maeda, Junjiro Noguchi, Alan Weinstein

This quantity is devoted to the reminiscence of Shoshichi Kobayashi, and gathers contributions from exotic researchers engaged on subject matters with reference to his study components. The publication is geared up into 3 elements, with the 1st half featuring an outline of Professor Shoshichi Kobayashi’s profession. this is often via expository path lectures (the moment half) on contemporary subject matters in extremal Kähler metrics and price distribution thought, so one can be useful for graduate scholars in arithmetic attracted to new subject matters in advanced geometry and intricate research. finally, the 3rd a part of the amount collects authoritative study papers on differential geometry and intricate analysis.

Professor Shoshichi Kobayashi was once a famous overseas chief within the parts of differential and complicated geometry. He contributed an important principles which are nonetheless thought of primary in those fields. The publication may be of curiosity to researchers within the fields of differential geometry, complicated geometry, and a number of other advanced variables geometry, in addition to to graduate scholars in mathematics.

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Download An Introduction to Noncommutative Geometry by Joseph C. Varilly PDF

By Joseph C. Varilly

Noncommutative geometry, encouraged through quantum physics, describes singular areas by means of their noncommutative coordinate algebras and metric constructions through Dirac-like operators. Such metric geometries are defined mathematically through Connes' thought of spectral triples. those lectures, introduced at an EMS summer time tuition on noncommutative geometry and its functions, offer an summary of spectral triples in keeping with examples. This advent is geared toward graduate scholars of either arithmetic and theoretical physics. It offers with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, motion functionals, and isospectral deformations. The structural framework is the concept that of a noncommutative spin geometry; the stipulations on spectral triples which ascertain this idea are built intimately. The emphasis all through is on gaining figuring out through computing the main points of particular examples. The booklet offers a center floor among a complete textual content and a narrowly concentrated study monograph. it truly is meant for self-study, allowing the reader to achieve entry to the necessities of noncommutative geometry. New gains because the unique path are an accelerated bibliography and a survey of newer examples and purposes of spectral triples. A ebook of the eu Mathematical Society (EMS). dispensed in the Americas by means of the yank Mathematical Society.

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Download Seifert fiberings by Kyung Bai Lee, Frank Raymond PDF

By Kyung Bai Lee, Frank Raymond

Seifert fiberings expand the idea of fiber package deal mappings by way of permitting the various fibers to be singular. clear of the singular fibers, the fibering is a regular package with fiber a set homogeneous house. The singular fibers are quotients of this homogeneous house by way of uncommon teams of homeomorphisms. those fiberings are ubiquitous and critical in arithmetic. This ebook describes in a unified approach their constitution, how they come up, and the way they're categorized and utilized in purposes. Manifolds owning such fiber constructions are mentioned and diversity from the classical three-d Seifert manifolds to raised dimensional analogues encompassing, for instance, flat manifolds, infra-nil-manifolds, area varieties, and their moduli areas. the mandatory instruments no longer lined in simple graduate classes are handled in huge element. those contain transformation teams, cohomology of teams, and wanted Lie idea. Inclusion of the Bieberbach theorems, life, distinctiveness, and pressure of Seifert fiberings, aspherical manifolds, symmetric areas, toral rank of round house varieties, equivariant cohomology, polynomial buildings on solv-manifolds, fastened element concept, and different examples, routines and functions attest to the breadth of those fiberings. this can be the 1st time the scattered literature on singular fiberings is introduced jointly in a unified technique. the hot tools and instruments hired could be invaluable to researchers and scholars drawn to geometry and topology

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Download Analysis and Algebra on Differentiable Manifolds: A Workbook by Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk PDF

By Pedro M. Gadea, Jaime Muñoz Masqué, Ihor V. Mykytyuk

This is the second one version of this top promoting challenge e-book for college students, now containing over four hundred thoroughly solved routines on differentiable manifolds, Lie idea, fibre bundles and Riemannian manifolds.

The workouts pass from common computations to particularly refined instruments. some of the definitions and theorems used all through are defined within the first element of each one bankruptcy the place they appear.

A 56-page number of formulae is integrated which might be priceless as an aide-mémoire, even for lecturers and researchers on these topics.

In this 2d edition:
• seventy six new difficulties
• a piece dedicated to a generalization of Gauss’ Lemma
• a quick novel part facing a few homes of the strength of Hopf vector fields
• an increased selection of formulae and tables
• a longer bibliography

Audience

This ebook should be beneficial to complicated undergraduate and graduate scholars of arithmetic, theoretical physics and a few branches of engineering with a rudimentary wisdom of linear and multilinear algebra.

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Download An Introduction to Noncommutative Differential Geometry and by J. Madore PDF

By J. Madore

This is often an creation to noncommutative geometry, with designated emphasis on these instances the place the constitution algebra, which defines the geometry, is an algebra of matrices over the complicated numbers. functions to straightforward particle physics also are mentioned. This moment version is carefully revised and contains new fabric on fact stipulations and linear connections plus examples from Jordanian deformations and quantum Euclidean areas. just some familiarity with traditional differential geometry and the speculation of fiber bundles is thought, making this publication obtainable to graduate scholars and novices to this box.

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Download Global Riemannian Geometry: Curvature and Topology by Steen Markvorsen PDF

By Steen Markvorsen

The ebook incorporates a transparent exposition of 2 modern subject matters in glossy differential geometry:

- distance geometric research on manifolds, particularly, comparability concept for distance services in areas that have good outlined bounds on their curvature
- the applying of the Lichnerowicz formulation for Dirac operators to the research of Gromov's invariants to degree the K-theoretic dimension of a Riemannian manifold.

It is meant for either graduate scholars and researchers who are looking to get a short and glossy advent to those topics.

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