Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.
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0 of 1 people found the following review helpful:
5.0 out of 5 stars
A very nice introduction,
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This review is from: Cohomology of Groups (Graduate Texts in Mathematics, No. 87) (Hardcover)
The subject is rather abstract, but the author does an excellent job of motivating it. I would recommend you read it together with Weibel's excellent (but somewhat less motivated)An Introduction to Homological Algebra (Cambridge Studies in Advanced Mathematics)
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We collect here for ease of reference some terminology and results concerning chain complexes. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
virtual duality group, cochain cup product, homological type, ordered simplicial complex, periodic cohomology, upper triangular group, finite projective resolution, homological functor, augmented chain complex, crossed module, dualizing module, duality groups, cohomology version, commutes with direct limits, relative homological algebra, contracting homotopy, equivariant homology, cellular chain complex, cochain level, long exact homology sequence, cap product, cohomological dimension, coefficient module, chain map, augmented complex Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hattori Stallings, Mayer Vietoris, Use the Mayer-Vietoris New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
We collect here for ease of reference some terminology and results concerning chain complexes. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
virtual duality group, cochain cup product, homological type, ordered simplicial complex, periodic cohomology, upper triangular group, finite projective resolution, homological functor, augmented chain complex, crossed module, dualizing module, duality groups, cohomology version, commutes with direct limits, relative homological algebra, contracting homotopy, equivariant homology, cellular chain complex, cochain level, long exact homology sequence, cap product, cohomological dimension, coefficient module, chain map, augmented complex Key Phrases - Capitalized Phrases (CAPs): (learn more)
Hattori Stallings, Mayer Vietoris, Use the Mayer-Vietoris New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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100
books
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- Cyclotomic Fields (Graduate Texts in Mathematics) by S. Lang in Front Matter, Back Matter (1), and Back Matter (2)
- Linear Algebra: Supplementary Notes & Problems by E. L. Cohen in Front Matter, and Back Matter
- Functions of One Complex Variable (Graduate Texts in Mathematics - Vol 11) (v. 1) by John B Conway in Front Matter, and Back Matter
- The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics) (v. 106) by Joseph H. Silverman in Back Matter (1), and Back Matter (2)
- Algebraic Geometry (Graduate Texts in Mathematics) by Robin Hartshorne in Front Matter
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- Algebra And Number Theory (Lecture Notes in Pure and Applied Mathematics) by Mohammed Boulagouaz on page 225, page 262, and page 271
- Geometry and Cohomology in Group Theory (London Mathematical Society Lecture Note Series) by Peter H. Kropholler on page 9, and page 106
- Algorithmic Problems in Groups and Semigroups (Trends in Mathematics) by Jean-Camille Birget on page 84, and page 214
- Computers, Rigidity, and Moduli: The Large-Scale Fractal Geometry of Riemannian Moduli Space (Porter Lectures) by Shmuel Weinberger on page 65, and Back Matter
- A Course in Homological Algebra (Graduate Texts in Mathematics) by Peter J. Hilton on page 343, and Back Matter
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