By Marcelo Aguilar, Samuel Gitler, Carlos Prieto
The authors current introductory fabric in algebraic topology from a unique perspective in utilizing a homotopy-theoretic strategy. This conscientiously written e-book could be learn through any pupil who is familiar with a few topology, supplying an invaluable strategy to quick research this novel homotopy-theoretic viewpoint of algebraic topology.
From the reviews:
"This is a easy direction on algebraic topology and … it really is excellently written and composed and will be strongly instructed to anyone wishing to profit the sector. The reader can locate many examples, calculations, and likewise a few routines. … The publication has appendices, … references together with eighty three goods and an extended checklist of symbols. there are various comments and reviews making the orientation of the reader within the box of algebraic topology more straightforward … ." (EMS, June, 2004)
"The modus operandi of algebraic topology is to affiliate algebraic invariants, resembling teams or jewelry, to a topological area in this kind of means that identical areas express isomorphic invariants; the following, ‘equivalent’ can be selected to slot the geometry of the matter. during this ebook, ‘equivalent’ ability homotopy identical … . For its readability and directness, a welcome boost to complex arithmetic collections. Upper-division undergraduates via faculty." (J. McCleary, selection, December, 2002)
"The function of this e-book is to introduce algebraic topology utilizing the radical procedure of homotopy thought … . the elemental thoughts 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 strategy 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 no longer often coated by way of a primary ebook in algebraic topology … . The textual content is thoroughly good written. … the scholar in algebraic topology will locate within the e-book loads of attention-grabbing well-exposed material.” (Yves Félix, Bulletin of the Belgian Mathematical Society, 2007)
From the again Cover
The function of this publication is to introduce algebraic topology utilizing the unconventional strategy of homotopy thought, an procedure with transparent purposes in algebraic geometry as understood via Lawson and Voevodsky. this technique permits the authors to hide the fabric extra successfully than the extra universal strategy utilizing homological algebra. the elemental thoughts of homotopy thought, equivalent to fibrations and cofibrations, are used to build singular homology and cohomology, in addition to K-theory. in the course of the textual content many different primary options are brought, together with the development of the attribute periods of vector bundles. even supposing functors look regularly through the textual content, no wisdom approximately type concept is anticipated from the reader. This e-book is meant for complex undergraduates and graduate scholars with a simple wisdom of aspect set topology in addition to workforce thought 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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Additional info for Algebraic Topology from a Homotopical Viewpoint (Universitext)
31) Beweis: Zu (27): Für n=1 trivial. A. Vo, VI, V2 Einheitsvektoren (vgl. (25))], daß aus dem Additionstheorem für cos mittels (22) und unter Benutzung von (14),(15) folgt, daß die Funktion cos auf den zwei Seiten der Kongruenz (27) den gleichen Wert annimmt. Analoges folgt mittels (14),(18),(4) für sin . Damit ist (27) für n=2 gezeigt; dann Induktion über n. - Zu (29): Nach (27) gilt: 1:o(v,a)+ 1:o(a,w) == 1:o(v,w) mod211'. Andererseits ist die linke bzw. rechte Seite der letzten Kongruenz zufolge (28),(24), bzw.
Folgere aus (1) bzw. (2): J hat nur die Eigenwerte ± i E Seien