By Marcelo Aguilar, Samuel Gitler, Carlos Prieto

ISBN-10: 0387954503

ISBN-13: 9780387954509

The authors current introductory fabric in algebraic topology from a singular viewpoint in utilizing a homotopy-theoretic strategy. This conscientiously written e-book could be learn through any pupil who understands a few topology, offering an invaluable way to fast study this novel homotopy-theoretic viewpoint of algebraic topology.

From the reviews:

"This is a simple direction on algebraic topology and … it's excellently written and composed and will be strongly suggested to anyone wishing to profit the sector. The reader can locate many examples, calculations, and likewise a few routines. … The booklet has appendices, … references which include eighty three goods and a protracted 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, equivalent to teams or jewelry, to a topological area in this kind of manner that identical areas show isomorphic invariants; right here, ‘equivalent’ can be selected to slot the geometry of the matter. during this booklet, ‘equivalent’ skill homotopy an identical … . For its readability and directness, a great addition to complex arithmetic collections. Upper-division undergraduates via faculty." (J. McCleary, selection, December, 2002)

"The objective of this ebook is to introduce algebraic topology utilizing the radical method of homotopy thought … . the fundamental innovations of homotopy concept … are used to build singular homology and cohomology, in addition to K-theory. … in the course of the textual content many different basic strategies are brought … ." (L’Enseignement Mathematique, Vol. forty eight (3-4), 2002)

“The publication of Aguilar, Gitler and Prieto offers an engaging new process for a primary path in algebraic topology. … what's additionally very fascinating is the truth that the ebook features a distinctive presentation of a few deep result of algebraic topology no longer frequently lined by way of a primary e-book in algebraic topology … . The textual content is punctiliously good written. … the coed in algebraic topology will locate within the ebook loads of fascinating 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 radical method 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 fundamental suggestions of homotopy thought, resembling fibrations and cofibrations, are used to build singular homology and cohomology, in addition to K-theory. during the textual content many different basic ideas are brought, together with the development of the attribute periods of vector bundles. even if functors look consistently in the course of the textual content, no wisdom approximately type idea is anticipated from the reader. This e-book is meant for complicated undergraduates and graduate scholars with a simple wisdom of element set topology in addition to crew concept 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)**

**Sample text**

77) when = −1. t 5th-order 10th-order 15th-order 20th-order exact approx. approx. approx. approx. 84) when = −1. t 10th-order 20th-order 40th-order 50th-order exact approx. approx. approx. approx. 100) when = −1 and α = ±1/2, ±π/4. 101) when = −1/2 and α = ±1/2, ±π/4. 69). 78). 57). 57) when = −1/10. 69) when H(t) = 1/(1 + t). Dash-dotted line: 20th-order approximation of V (0); solid line: 20th-order approximation of V (0). 77) when H(t) = exp(−t). Dash-dotted line: 10th-order approximation of V (0); solid line: 20th-order approximation of V (0); dashed lined: 10th-order approximation of V (0); dash-dot-dotted line: 20th-order approximation of V (0).

T 10th-order 20th-order 40th-order 60th-order exact approx. approx. approx. approx. 77) for diﬀerent values of . 77) for diﬀerent values of . 77) when = −1. t 5th-order 10th-order 15th-order 20th-order exact approx. approx. approx. approx. 84) when = −1. t 10th-order 20th-order 40th-order 50th-order exact approx. approx. approx. approx. 100) when = −1 and α = ±1/2, ±π/4. 101) when = −1/2 and α = ±1/2, ±π/4. 69). 78). 57). 57) when = −1/10. 69) when H(t) = 1/(1 + t). Dash-dotted line: 20th-order approximation of V (0); solid line: 20th-order approximation of V (0).

Approx. 100) when = −1 and α = ±1/2, ±π/4. 101) when = −1/2 and α = ±1/2, ±π/4. 69). 78). 57). 57) when = −1/10. 69) when H(t) = 1/(1 + t). Dash-dotted line: 20th-order approximation of V (0); solid line: 20th-order approximation of V (0). 77) when H(t) = exp(−t). Dash-dotted line: 10th-order approximation of V (0); solid line: 20th-order approximation of V (0); dashed lined: 10th-order approximation of V (0); dash-dot-dotted line: 20th-order approximation of V (0). 8). 8). 99) at the 31st-order of approximation when α = π/4.

### Algebraic Topology from a Homotopical Viewpoint (Universitext) by Marcelo Aguilar, Samuel Gitler, Carlos Prieto

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