| 000 | 03619nam a2200409Ii 4500 | ||
|---|---|---|---|
| 001 | 9780429100475 | ||
| 008 | 180611s2013 fluab ob 001 0 eng d | ||
| 020 |
_a9780429100475 _q(e-book : PDF) |
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| 035 | _a(OCoLC)916120021 | ||
| 040 |
_aFlBoTFG _cFlBoTFG _erda |
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| 050 | 4 | _aQA612 | |
| 072 | 7 |
_aMAT _x002000 _2bisacsh |
|
| 072 | 7 |
_aMAT _x012000 _2bisacsh |
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| 072 | 7 |
_aPBM _2bicscc |
|
| 082 | 0 | 4 |
_a514/.2 _223 |
| 100 | 1 |
_aShastri, Anant Ram, _d1920- _eauthor. _911376 |
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| 245 | 1 | 0 |
_aBasic algebraic topology / _cby Anant R. Shastri. |
| 250 | _aFirst edition. | ||
| 264 | 1 |
_aBoca Raton, FL : _bChapman and Hall/CRC, an imprint of Taylor and Francis, _c2013. |
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| 300 |
_a1 online resource (551 pages) : _b61 illustrations |
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| 336 |
_atext _2rdacontent |
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| 337 |
_acomputer _2rdamedia |
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| 338 |
_aonline resource _2rdacarrier |
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| 505 | 0 | _achapter 1 Introduction -- chapter 2 Cell Complexes and Simplicial Complexes -- chapter 3 Covering Spaces and Fundamental Group -- chapter 4 Homology Groups -- chapter 5 Topology of Manifolds -- chapter 6 Universal Coefficient Theorem for Homology -- chapter 7 Cohomology -- chapter 8 Homology of Manifolds -- chapter 9 Cohomology of Sheaves -- chapter 10 Homotopy Theory -- chapter 11 Homology of Fibre Spaces -- chapter 12 Characteristic Classes -- chapter 13 Spectral Sequences. | |
| 520 | 3 | _aBuilding on rudimentary knowledge of real analysis, point-set topology, and basic algebra, Basic Algebraic Topology provides plenty of material for a two-semester course in algebraic topology. The book first introduces the necessary fundamental concepts, such as relative homotopy, fibrations and cofibrations, category theory, cell complexes, and simplicial complexes. It then focuses on the fundamental group, covering spaces and elementary aspects of homology theory. It presents the central objects of study in topology visualization: manifolds. After developing the homology theory with coefficients, homology of the products, and cohomology algebra, the book returns to the study of manifolds, discussing Poincaré duality and the De Rham theorem. A brief introduction to cohomology of sheaves and ?ech cohomology follows. The core of the text covers higher homotopy groups, Hurewicz's isomorphism theorem, obstruction theory, Eilenberg-Mac Lane spaces, and Moore-Postnikov decomposition. The author then relates the homology of the total space of a fibration to that of the base and the fiber, with applications to characteristic classes and vector bundles. The book concludes with the basic theory of spectral sequences and several applications, including Serre's seminal work on higher homotopy groups.Thoroughly classroom-tested, this self-contained text takes students all the way to becoming algebraic topologists. Historical remarks throughout the text make the subject more meaningful to students. Also suitable for researchers, the book provides references for further reading, presents full proofs of all results, and includes numerous exercises of varying levels. | |
| 650 | 7 |
_aMATHEMATICS / Geometry / General. _2bisacsh _910959 |
|
| 650 | 0 |
_aAlgebraic topology _xTextbooks. _911377 |
|
| 650 | 0 |
_aAlgebraic topology. _911378 |
|
| 650 | 0 |
_aAlgebraische Topologie. _911379 |
|
| 650 | 7 |
_aMATHEMATICS / Topology. _2bisacsh _911380 |
|
| 650 | 7 |
_aMATHEMATICS _xAlgebra _vGeneral. _2bisacsh _911381 |
|
| 650 | 7 |
_aMATHEMATICS _xGeometry _vGeneral. _2bisacsh _911382 |
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| 710 | 2 |
_aTaylor and Francis. _910719 |
|
| 776 | 0 | 8 |
_iPrint version: _z9781466562431 |
| 856 | 4 | 0 |
_uhttps://www.taylorfrancis.com/books/9781466562448 _zClick here to view. |
| 942 | _cEBK | ||
| 999 |
_c69954 _d69954 |
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