Books > Science & Mathematics > Mathematics > Topology
|
Buy Now
Topology and Groupoids (Paperback, REV Updtd & Exp Ver ed.)
Loot Price: R890
Discovery Miles 8 900
|
|
Topology and Groupoids (Paperback, REV Updtd & Exp Ver ed.)
Expected to ship within 10 - 15 working days
|
This is the third edition of a classic text, previously published
in 1968, 1988, and now extended, revised, retitled, updated, and
reasonably priced. Throughout it gives motivation and context for
theorems and definitions. Thus the definition of a topology is
first related to the example of the real line; it is then given in
terms of the intuitive notion of neighbourhoods, and then shown to
be equivalent to the elegant but spare definition in terms of open
sets. Many constructions of topologies are shown to be necessitated
by the desire to construct continuous functions, either from or
into a space. This is in the modern categorical spirit, and often
leads to clearer and simpler proofs. There is a full treatment of
finite cell complexes, with the cell decompositions given of
projective spaces, in the real, complex and quaternionic cases.
This is based on an exposition of identification spaces and
adjunction spaces. The exposition of general topology ends with a
description of the topology for function spaces, using the modern
treatment of the test-open topology, from compact Hausdorff spaces,
and so a description of a convenient category of spaces (a term due
to the author) in the non Hausdorff case. The second half of the
book demonstrates how the use of groupoids rather than just groups
gives in 1-dimensional homotopy theory more powerful theorems with
simpler proofs. Some of the proofs of results on the fundamental
groupoid would be difficult to envisage except in the form given:
We verify the required universal property'. This is in the modern
categorical spirit. Chapter 6 contains the development of the
fundamental groupoid on a set of base points, including the
background in category theory. The proof of the van Kampen Theorem
in this general form resolves a failure of traditional treatments,
in giving a direct computation of the fundamental group of the
circle, as well as more complicated examples. Chapter 7 uses the
notion of cofibration to develop the notion of operations of the
fundamental groupoid on certain sets of homotopy classes. This
allows for an important theorem on gluing homotopy equivalences by
a method which gives control of the homotopies involved. This
theorem first appeared in the 1968 edition. Also given is the
family of exact sequences arising from a fibration of groupoids.
The development of Combinatorial Groupoid Theory in Chapter 8
allows for unified treatments of free groups, free products of
groups, and HNN-extensions, in terms of pushouts of groupoids, and
well models the topology of gluing spaces together. These methods
lead in Chapter 9 to results on the Phragmen-Brouwer Property, with
a Corollary that the complement of any arc in an n-sphere is
connected, and then to a proof of the Jordan Curve Theorem. Chapter
10 on covering spaces is again fully in the base point free spirit;
it proves the natural theorem that for suitable spaces X, the
category of covering spaces of X is equivalent to the category of
covering morphisms of the fundamental groupoid of X. This approach
gives a convenient way of obtaining covering maps from covering
morphisms, and leads easily to traditional results using operations
of the fundamental group. Results on pullbacks of coverings are
proved using a Mayer-Vietoris type sequence. No other text treats
the whole theory directly in this way. Chapter 11 is on Orbit
Spaces and Orbit Groupoids, and gives conditions for the
fundamental groupoid of the orbit space to be the orbit groupoid of
the fundamental groupoid. No other topology text treats this
important area. Comments on the relations to the literature are
given in Notes at the end of each Chapter. There are over 500
exercises, 114 figures, numerous diagrams. See http:
//www.bangor.ac.uk/r.brown/topgpds.html for more information. See
http: //mathdl.maa.org/mathDL/19/?rpa=reviews&sa=viewBook&
bookId=69421 for a Mathematical Association of America review.
General
Imprint: |
Booksurge Llc
|
Country of origin: |
United States |
Release date: |
February 2006 |
First published: |
February 2006 |
Authors: |
Ronald Brown.
|
Dimensions: |
229 x 152 x 28mm (L x W x T) |
Format: |
Paperback
|
Pages: |
536 |
Edition: |
REV Updtd & Exp Ver ed. |
ISBN-13: |
978-1-4196-2722-4 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Topology >
General
|
LSN: |
1-4196-2722-8 |
Barcode: |
9781419627224 |
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
You might also like..
|