Algebraic Topology (EMS Textbooks in Mathematics) by Tammo Tom Dieck

By Tammo Tom Dieck

This booklet is written as a textbook on algebraic topology. the 1st half covers the fabric for 2 introductory classes approximately homotopy and homology. the second one half offers extra complicated functions and ideas (duality, attribute sessions, homotopy teams of spheres, bordism). the writer recommends beginning an introductory path with homotopy thought. For this objective, classical effects are awarded with new uncomplicated proofs. however, you could commence extra often with singular and axiomatic homology. extra chapters are dedicated to the geometry of manifolds, mobilephone complexes and fibre bundles. a distinct characteristic is the wealthy provide of approximately 500 routines and difficulties. numerous sections comprise themes that have no longer seemed sooner than in textbooks in addition to simplified proofs for a few vital effects. necessities are commonplace aspect set topology (as recalled within the first chapter), user-friendly algebraic notions (modules, tensor product), and a few terminology from type thought. the purpose of the e-book is to introduce complicated undergraduate and graduate (master's) scholars to uncomplicated instruments, techniques and result of algebraic topology. adequate history fabric from geometry and algebra is incorporated. A booklet of the ecu Mathematical Society (EMS). disbursed in the Americas via the yankee Mathematical Society.

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Thank you anon for the djvu add, I simply switched over and did ocr with tesseract. I didn't like Munkres type (too verbose imo) this one is far better.

-- Reviews

when i used to be a scholar, this and Munkres have been the topology books opposed to which each and every different ebook was once measured.

And whereas Munkres used to be of a extra introductory style, this was once the genuine deal.


There are just a number of vintage encyclopaedic texts on undergraduate topology, and Dugundji's is considered one of them. And between such books, this can be my favorite as the others are too out of date or too voluminous. Dugundji's ebook is brief, glossy, and impeccable. It covers each subject an undergraduate should still comprehend or even extra. it's nonetheless valuable for me after years of use. It exposes all very important strategies of set topology and provides a quick yet centred creation to algebraic topology.
You won't remorse to learn it.


One of the easiest Topology books i've got learn. even if the ebook has no figures (as one might anticipate from a topology book), virtually each element is roofed and there usually are not imprecise components within the proofs. for instance, the publication through Willard can be solid, yet in a few elements there are extra complicated information left for the reader. I took a simple topology graduate point direction at the first half 2007, which consisted on fixing the issues during this e-book. We have been capable of finding a few difficulties that requested to end up anything fake, yet they have been 3 or 4 between all of the difficulties from sections III to VIII. besides, this booklet is a vintage that you can personal if you happen to plan to paintings in topology or at the very least learn it whereas learning the topic. It's only a disgrace that the ebook is out of print.

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Extra resources for Algebraic Topology (EMS Textbooks in Mathematics)

Example text

The choice of a base point is an additional structure. , to X with an additional base point added (topological sum), with the obvious extension to pointed maps. This functor is compatible with homotopies. We also have the forgetful functor ˇ from TOP0 to TOP. X; ˇY /, and similarly for the homotopy categories. The category TOP0 has sums and products. Xj ; xj / is a family of pointed spaces. xj / of base points Wis taken as base point in the`product Q j Xj ; this yields the pointed product. Let j 2J Xj be the quotient of j 2J Xj where all base points are W identified to a single new base point.

Z; X/ ! Y; Z/ ! X; Z/ are h-equivalences. Z; X / ! Y; Z/ ! X; Z/ are pointed h-equivalences. Problems 1. Verify that f Z and Z f are continuous. 2. An inclusion i W Z Y`induces an embedding i X W ZX ! Y X . Q 3. Xj ; Y / is always a homeomorphism. Q 4. X; j Yj / ! X; Yj /, f 7! prj f / is always bijective and continuous. If X is locally compact, it is a homeomorphism. 5. Let p W X ! Y be a surjective continuous map. Suppose the pre-image of a compact set is compact. Then Z p W Z Y ! Z X is an embedding.

CnC1 /. Finally, one can define the quaternionic projective space HP n in a similar manner as a quotient of HnC1 X 0 or as a quotient of S 4nC3 . We generalize projective spaces. Let W be an n-dimensional real vector space. W / the set of k-dimensional subspaces of W . W /. Suppose W carries an inner product. w1 ; : : : ; wk / in W considered as a subspace of W k . W / the Stiefel manifold of orthonormal k-frames in W . W / ! w1 ; : : : ; wk / to the subspace Œw1 ; : : : ; wk  spanned by this sequence.

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