By Marcelo Aguilar, Samuel Gitler, Carlos Prieto

The authors current introductory fabric in algebraic topology from a unique standpoint in utilizing a homotopy-theoretic method. This rigorously written ebook might be learn through any scholar who is aware a few topology, delivering an invaluable strategy to quick examine this novel homotopy-theoretic standpoint of algebraic topology.

From the reviews:

"This is a easy path on algebraic topology and … it truly is excellently written and composed and will be strongly prompt to anyone wishing to benefit the sphere. The reader can locate many examples, calculations, and likewise a couple of workouts. … The booklet has appendices, … references such as eighty three goods and a protracted record of symbols. there are lots of comments and reviews making the orientation of the reader within the box of algebraic topology more uncomplicated … ." (EMS, June, 2004)

"The modus operandi of algebraic topology is to affiliate algebraic invariants, similar to teams or earrings, to a topological area in this kind of method that an identical areas convey isomorphic invariants; right here, ‘equivalent’ could be selected to slot the geometry of the matter. during this e-book, ‘equivalent’ capacity homotopy similar … . For its readability and directness, a welcome boost to complex arithmetic collections. Upper-division undergraduates via faculty." (J. McCleary, selection, December, 2002)

"The goal of this e-book is to introduce algebraic topology utilizing the unconventional method of homotopy concept … . the elemental recommendations of homotopy concept … are used to build singular homology and cohomology, in addition to K-theory. … during the textual content many different basic options are brought … ." (L’Enseignement Mathematique, Vol. forty eight (3-4), 2002)

“The publication of Aguilar, Gitler and Prieto supplies an attractive new procedure for a primary path in algebraic topology. … what's additionally very fascinating is the truth that the ebook includes a exact presentation of a few deep result of algebraic topology now not often lined by way of a primary e-book in algebraic topology … . The textual content is punctiliously good written. … the scholar in algebraic topology will locate within the e-book loads of fascinating well-exposed material.” (Yves Félix, Bulletin of the Belgian Mathematical Society, 2007)

From the again Cover

The goal of this booklet is to introduce algebraic topology utilizing the radical process of homotopy idea, an method with transparent purposes in algebraic geometry as understood via Lawson and Voevodsky. this system permits the authors to hide the cloth extra successfully than the extra universal process utilizing homological algebra. the elemental options of homotopy thought, comparable to fibrations and cofibrations, are used to build singular homology and cohomology, in addition to K-theory. through the textual content many different primary options are brought, together with the development of the attribute periods of vector bundles. even though functors seem continuously in the course of the textual content, no wisdom approximately class thought is predicted from the reader. This ebook is meant for complicated undergraduates and graduate scholars with a simple wisdom of aspect set topology in addition to team conception and will be utilized in a semester course.

Marcelo Aguilar and Carlos Prieto are Professors on the Instituto de Matemticas, Universidad Nacional Autónoma de México, and Samuel Gitler is a member of El Colegio Nacional and professor on the Centro de Investigación y Estudios Avanzados del IPN.

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**Sample text**

3. BROÜWKR. (Communicated by Prof. KORTEWRG). As the position of S4 is determined with respect to a fixed system of axes by sic independent variables and that of S* with respect to a fixed system of axes by three independent variables we understand at once that in an infinite number of ways two S9 motions can be coordinated to an S4 motion, so that position and velocities of>S4are determined by position and velocities of the two >S3's. On such a coordination Mr. JAHNKK has been engaged in the papers mentioned above and has deduced the relations between positions and velocities of S4 and the two >Ç8's.

As moreover the *23 " Γ *14 ' k 31 ~ T ' k 2 4 ' k 12 ~T C71 m of a plane are the cosines of direction of the représentant of the system equiangular to the right with that plane with respect to the system of axes OX> Yr Zr (defined Proceedings Marcli'1904, p. 72b), and likewise *23 *14 *31 'k2 4 *12 *34 the cosines of direction of the représentant of the system equiangular to the left with that plane with respect to the system of axes OXi Yi Zi (defined in the same place) the Sr and Si introduced just now prove to be identical with those introduced here formerly (see Proceedings March, 1904, p.

Proof. P=V. is its potential. For v 3 P = V F , or V ( \ 7 P ) = V F , or Farther follows out of the field property of V, that P is uniformly determined as V"" 2 of V V, so as V of V. So P has clearly the potential property; it need, however, not have the field property. B. A distribution not to be regarded here, because it has not the field property, though it has the potential property, is e. g. the fictitious force field of a single agens point in £ 3 . For, here we have not a potential vanishing at infinity — and as such determined uniformly.