Fibre BundlesFibre bundles play an important role in just about every aspect of modern geometry and topology. Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical physics. In this third edition two new chapters on the gauge group of a bundle and on the differential forms representing characteristic classes of complex vector bundles on manifolds have been added. These chapters result from the important role of the gauge group in mathematical physics and the continual usefulness of characteristic classes defined with connections on vector bundles. |
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Ostala izdanja - Prikaži sve
Uobičajeni izrazi i fraze
algebra B-morphism base point bijection calculate characteristic classes Chern classes clutching map cofunctor cohomology commutative diagram compact complex vector bundle Corollary cross section CW-complex defined Definition denote dimension elements equals exact sequence exists fibre bundle fibre homotopy fibre map finite following commutative diagram following diagram functor G-module G-space Gk(F H-space homeomorphism homotopy classes homotopy equivalence Hopf invariant inclusion induced isomorphism classes Let f line bundle linear locally trivial manifold map f maximal torus module monomorphism Moreover multiplication nonzero notations orientation orthogonal paracompact space phism polynomial principal G-bundle Proof properties proves the proposition proves the theorem quotient real vector bundle relation Remark representation ring restriction result s e G semigroup semiring Spin(n statement Stiefel-Whitney class subgroup subspace tangent bundle theory topology total space transition functions trivial bundle UF(n unique vector bundle morphism vector fields vector space Weyl group
Popularni odlomci
Stranica 239 - We are now in a position to prove the main theorem of this section. THEOREM I.
Stranica 346 - I'existence d'un champ d'elements de contact on d'une structure complex sur une sphere. CR Acad. Sci. Paris, 226 (1948), 2117-2119. 108. *On the product of sphere bundles and the duality theorem modulo two.
Stranica 346 - Espaces fibres en spheres et carres de Steenrod. Ann. Ecole Norm. Sup., 69 (1952), 109-181.
Stranica 4 - K is a compact subset of X, and V is an open neighborhood of 0, then there exists e > 0 such that SK c V whenever \S\ < €. PROOF.
Stranica 341 - Borel. A., and F. Hirzebruch: 1. Characteristic classes and homogeneous spaces: I, II. III. Am. J. Math, 80: 458-538 (1958). 81: 31 5-382 (1959).
Stranica 187 - Now we are able to state and prove the main result of this section, by removing the stabilizability assumption in Theorem 7.6.3.
Stranica 345 - The Topology of Fibre Bundles, Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1951. 9. Ju. V. Zjuzin and V. Ja. Lin, Unramified algebraic extensions of commutati<* Banach algebras, Mat. Sb., 91 (133) (1973). 402-420. = Math. USSR Sbornik, 20 (1973'.
Stranica 20 - B are locally isomorphic provided for each be B there exists an open neighborhood U of b such that c\U and n\U are U-isomorphic.
Stranica 339 - USA. 39: 636-638 (1953). 3. The relations on Steenrod powers of cohomology classes, in "Algebraic Geometry and Topology. A Symposium in Honor of S. Lefschetz.
Stranica 115 - This ~ is an equivalence relation. Let a - b denote the equivalence class of a pair (a, 6).
Reference za ovu knjigu
Bibliografski podaci
| Naslov | Fibre Bundles Opseg 20 iz Graduate Texts in Mathematics, ISSN 0072-5285 |
| Autori | Dale Husemoller, Dale Husemöller |
| Izdanje | ilustrirano |
| Izdavač | Springer Science & Business Media, 1994 |
| ISBN | 0387940871, 9780387940878 |
| Duljina | Broj stranica: 353 |
| Izvezi navode | BiBTeX EndNote RefMan |