# topology geometry and algebra

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## Topology Geometry And Algebra

**Author :**R. James Milgram

**ISBN :**9780821820636

**Genre :**Mathematics

**File Size :**56. 8 MB

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This volume presents the proceedings from the conference on ``Topology, Geometry, and Algebra: Interactions and New Directions'' held in honor of R. James Milgram at Stanford University in August 1999. The meeting brought together distinguished researchers from a variety of areas related to algebraic topology and its applications. Papers in the book present a wide range of subjects, reflecting the nature of the conference. Topics include moduli spaces, configuration spaces, surgery theory, homotopy theory, knot theory, group actions, and more. Particular emphasis was given to the breadth of interaction between the different areas.

## Algebraic Topology Via Differential Geometry

**Author :**M. Karoubi

**ISBN :**0521317142

**Genre :**Mathematics

**File Size :**29. 49 MB

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In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.

## Topological Methods In Algebraic Geometry

**Author :**Friedrich Hirzebruch

**ISBN :**9783662306970

**Genre :**Mathematics

**File Size :**44. 87 MB

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## Topological Geometry

**Author :**Ian R. Porteous

**ISBN :**0521298393

**Genre :**Mathematics

**File Size :**76. 69 MB

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Provides a route from first principles through standard linear and quadratic algebra to geometric algebra, with Clifford's geometric algebras taking pride of place.

## Bridging Algebra Geometry And Topology

**Author :**Denis Ibadula

**ISBN :**9783319091860

**Genre :**Mathematics

**File Size :**28. 3 MB

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Algebra, geometry and topology cover a variety of different, but intimately related research fields in modern mathematics. This book focuses on specific aspects of this interaction. The present volume contains refereed papers which were presented at the International Conference “Experimental and Theoretical Methods in Algebra, Geometry and Topology”, held in Eforie Nord (near Constanta), Romania, during 20-25 June 2013. The conference was devoted to the 60th anniversary of the distinguished Romanian mathematicians Alexandru Dimca and Ştefan Papadima. The selected papers consist of original research work and a survey paper. They are intended for a large audience, including researchers and graduate students interested in algebraic geometry, combinatorics, topology, hyperplane arrangements and commutative algebra. The papers are written by well-known experts from different fields of mathematics, affiliated to universities from all over the word, they cover a broad range of topics and explore the research frontiers of a wide variety of contemporary problems of modern mathematics.

## Topology And Geometry

**Author :**Glen E. Bredon

**ISBN :**9781475768480

**Genre :**Mathematics

**File Size :**71. 14 MB

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This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

## A Geometry Of Approximation

**Author :**Piero Pagliani

**ISBN :**9781402086229

**Genre :**Philosophy

**File Size :**73. 50 MB

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'A Geometry of Approximation' addresses Rough Set Theory, a field of interdisciplinary research first proposed by Zdzislaw Pawlak in 1982, and focuses mainly on its logic-algebraic interpretation. The theory is embedded in a broader perspective that includes logical and mathematical methodologies pertaining to the theory, as well as related epistemological issues. Any mathematical technique that is introduced in the book is preceded by logical and epistemological explanations. Intuitive justifications are also provided, insofar as possible, so that the general perspective is not lost. Such an approach endows the present treatise with a unique character. Due to this uniqueness in the treatment of the subject, the book will be useful to researchers, graduate and pre-graduate students from various disciplines, such as computer science, mathematics and philosophy. It features an impressive number of examples supported by about 40 tables and 230 figures. The comprehensive index of concepts turns the book into a sort of encyclopaedia for researchers from a number of fields. 'A Geometry of Approximation' links many areas of academic pursuit without losing track of its focal point, Rough Sets.

## Geometric And Algebraic Topological Methods In Quantum Mechanics

**Author :**G. Giachetta

**ISBN :**9789812561299

**Genre :**Science

**File Size :**87. 61 MB

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- The book collects all the advanced methods of quantization in the last decade. - It presents in a compact way all the necessary up to date mathematical tools to be used in studying quantum problems.

## Algebraic Topology

**Author :**William Fulton

**ISBN :**9781461241805

**Genre :**Mathematics

**File Size :**58. 98 MB

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To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: half of what one would like the student to know after a second course in topology)? Our answers to this have guided the choice of material, which includes: under standing the relation between homology and integration, first on plane domains, later on Riemann surfaces and in higher dimensions; wind ing numbers and degrees of mappings, fixed-point theorems; appli cations such as the Jordan curve theorem, invariance of domain; in dices of vector fields and Euler characteristics; fundamental groups

## Algebraic Geometry

**Author :**Solomon Lefschetz

**ISBN :**9780486154725

**Genre :**Mathematics

**File Size :**81. 12 MB

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An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.