Weakly Semialgebraic Spaces - Lecture Notes in Mathematics 1367 (Paperback)
  • Weakly Semialgebraic Spaces - Lecture Notes in Mathematics 1367 (Paperback)
zoom

Weakly Semialgebraic Spaces - Lecture Notes in Mathematics 1367 (Paperback)

(author)
£27.00
Paperback 378 Pages / Published: 22/02/1989
  • Not available

This product is currently unavailable.

  • This item has been added to your basket
The book is the second part of an intended three-volume treatise on semialgebraic topology over an arbitrary real closed field R. In the first volume (LNM 1173) the category LSA® or regular paracompact locally semialgebraic spaces over R was studied. The category WSA® of weakly semialgebraic spaces over R - the focus of this new volume - contains LSA® as a full subcategory. The book provides ample evidence that WSA® is "the" right cadre to understand homotopy and homology of semialgebraic sets, while LSA® seems to be more natural and beautiful from a geometric angle. The semialgebraic sets appear in LSA® and WSA® as the full subcategory SA® of affine semialgebraic spaces. The theory is new although it borrows from algebraic topology. A highlight is the proof that every generalized topological (co)homology theory has a counterpart in WSA® with in some sense "the same", or even better, properties as the topological theory. Thus we may speak of ordinary (=singular) homology groups, orthogonal, unitary or symplectic K-groups, and various sorts of cobordism groups of a semialgebraic set over R. If R is not archimedean then it seems difficult to develop a satisfactory theory of these groups within the category of semialgebraic sets over R: with weakly semialgebraic spaces this becomes easy. It remains for us to interpret the elements of these groups in geometric terms: this is done here for ordinary (co)homology.

Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
ISBN: 9783540508151
Number of pages: 378
Weight: 1230 g
Dimensions: 235 x 155 x 20 mm
Edition: 1989 ed.

You may also be interested in...

Riemann Surfaces
Added to basket
Fractals: A Very Short Introduction
Added to basket
Metric Spaces
Added to basket
Modern Graph Theory
Added to basket
Introduction to Topology
Added to basket
A Combinatorial Introduction to Topology
Added to basket
Algebraic Topology
Added to basket
£30.99
Paperback
Essential Topology
Added to basket
Knots
Added to basket
£16.95
Paperback
Knot Theory and Its Applications
Added to basket
Schaums Outline of General Topology
Added to basket

Reviews

Please sign in to write a review

Your review has been submitted successfully.