Last edited by Doll
Tuesday, October 6, 2020 | History

2 edition of Topics in the algebraic topology of the classical groups. found in the catalog.

Topics in the algebraic topology of the classical groups.

Sufian Yunis Husseini

Topics in the algebraic topology of the classical groups.

by Sufian Yunis Husseini

  • 268 Want to read
  • 18 Currently reading

Published by Dept. of Mathematics, University of Wisconsin in [Madison] .
Written in English

    Subjects:
  • Algebraic topology.

  • Edition Notes

    StatementLecture notes by Renzo Piccinini.
    ContributionsPiccinini, Renzo.
    The Physical Object
    Pagination1 v. (various pagings)
    ID Numbers
    Open LibraryOL16586473M

    This work may be used as the text for a one-semester graduate or advanced undergraduate course, as well as by students engaged in self-study. Requiring only minimal undergraduate prerequisites, 'Introduction to Manifolds' is also an excellent foundation for Springer's 'Differential Forms in Algebraic Topology'. Topology is a branch of mathematics concerned with geometrical properties objects that are insensitive to smooth deformations. This is most easily illustrated by the simple example of closed two-dimensional surfaces in three dimensions (see Fig. 1).A sphere can be smoothly deformed into many different shapes, such as the surface of a disk or a bowl.

    In mathematics, a topological group is a group G together with a topology on G such that both the group's binary operation and the function mapping group elements to their respective inverses are continuous functions with respect to the topology. A topological group is a mathematical object with both an algebraic structure and a topological structure. Thus, one may perform algebraic operations. After Peter May and Kate Ponto released their new book, there are very readable introductions to many of the topics on the "second level" of algebraic topology. There is a wonderful book on Cohomology Operations by Mosher and Tangora. It is thin (and only discusses one topic), but very nice. May & Ponto's new book is very nice. It covers three.

      Homology and cohomology were invented in (what's now called) the de Rham context, where cohomology classes are (classes of) differential forms and homology classes are (classes of) domains you can integrate them over. I think it's basically impos. More Concise Algebraic Topology: Localization, Completion, and Model Categories - Ebook written by J. P. May, K. Ponto. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read More Concise Algebraic Topology: Localization, Completion, and Model Categories.


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Topics in the algebraic topology of the classical groups by Sufian Yunis Husseini Download PDF EPUB FB2

Additional Physical Format: Online version: Husseini, Sufian Yunis, Topics in the algebraic topology of the classical groups. [Madison] Dept. of Mathematics, University of Wisconsin [].

Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups 5/5(1).

Topics in Classical Algebraic Geometry. This book explains the following topics: Polarity, Conics, Plane cubics, Determinantal equations, Theta characteristics, Plane Quartics, Planar Cremona transformations, Del Pezzo surfaces, Cubic surfaces, Geometry of Lines.

Author(s): Igor V. Dolgachev. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function.

This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail.

Originally published inthis book has become one of the seminal books. A Concise Course in Algebraic Topology (J. May) This book explains the following topics: The fundamental group and some of its applications, Categorical language and the van Kampen theorem, Covering spaces, Graphs, Compactly generated spaces, Cofibrations, Fibrations, Based cofiber and fiber sequences, Higher homotopy groups, CW complexes.

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups.

This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either 4/5(2). $\begingroup$ Hatcher's book is very well-written with a good combination of motivation, intuitive explanations, and rigorous details.

It would be worth a decent price, so it is very generous of Dr. Hatcher to provide the book for free download. But if you want an alternative, Greenberg and Harper's Algebraic Topology covers the theory in a straightforward and comprehensive manner.

Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.

Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function Brand: Springer India.

This book was written to be a readable introduction to algebraic topology with rather broad coverage of the subject. The viewpoint is quite classical in spirit, and stays well within the confines of pure algebraic topology.

In a sense, the book could have been written thirty or forty years ago since virtually everything in it is at least that old. Handbook of Algebraic Topology - Ebook written by I.M. James. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while you read Handbook of Algebraic Topology. The choice of topics covered in the book under review falls under what one may call classical algebraic topology.

The fundamental group, covering spaces, a heavy dose of homology theory, applications to manifolds, and the higher homotopy groups is what the book is all about. This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail.

Originally published inthis book has become one of the seminal : Springer Singapore. The book present original research on a wide range of topics in modern topology: the algebraic K-theory of spaces, the algebraic obstructions to surgery and finiteness, geometric and chain complexes, characteristic classes, and transformation groups.

Simplicial Objects in Algebraic Topology. Van Nostrand, Reprinted by University of Chicago Press, and [$20] • M Mimura and H Toda.

Topology of Lie Groups. Translations of Mathematical Monographs AMS, [$51] — Includes the algebraic topology proof of Bott Periodicity, as well as information about the five File Size: 65KB. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups.

This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism).

The author recommends starting an introductory course with homotopy theory. The book might well have been titled ‘What Every Young Topologist Should Know’ presents, in a self-contained and clear manner, all classical constituents of algebraic topology recommend this book as a valuable tool for everybody teaching graduate courses as well as a self-contained introduction for independent reading.Algebraic geometry and analytic geometry; Mirror symmetry; Algebraic groups.

Identity component; Linear algebraic group. Additive group; Multiplicative group; Algebraic torus; Reductive group; Borel subgroup; Parabolic subgroup; Radical of an algebraic group; Unipotent radical; Lie-Kolchin theorem; Haboush's theorem (also known as the Mumford.This isn't quite what you mean, but I took Igor Frenkel's algebraic topology course as an undergrad.

He taught out of Massey's book, A Basic Course in Algebraic Topology. It starts with the classification of 2-manifolds, does the fundamental group and the Seifert-von Kampen theorem, and then does singular homology and cohomology.