bibliography for K-theory and vector bundles

1 Bibliography for K-Theory and vector bundles

1.1 Books

M. F. Atiyah, K–Theory, W. A. Benjamin, 1967.

R. Bott, Lectures on K(X), W. A. Benjamin, 1969.

J. Dieudonné, A History of AlgebraicMathworldPlanetmath and Differential Topology 1900-1960, Birkhäuser, 1989.

W. Fulton, Young Tableaux, Cambridge Univ. Press, 1997.

H. Hiller, Geometry of Coxeter GroupsMathworldPlanetmath, Pitman, 1982.

D. Husemoller, Fibre Bundles, McGraw–Hill, 1966 (later editions by Springer-Verlag).

M. Karoubi, K–Theory: An Introduction, Springer–Verlag, 1978.

S. Lang, AlgebraPlanetmathPlanetmath, Addison–Wesley, 1965.

J. W. Milnor and J. D. Stasheff, Characteristic Classes, Princeton Univ. Press, 1974.

N. Steenrod, Topology of Fiber Bundles, Princeton Univ. Press, 1951.

R. Stong, Notes on Cobordism Theory, Princeton Univ. Press, 1968.

B. L. van der Waerden, Modern Algebra, Ungar, 1949.

1.2 Papers

J. F. Adams, On the non–existence of elements of Hopf invariant one, Ann. of Math. 72 (1960),20–104.

J. F. Adams, Vector fields on spheres, Ann. of Math. 75 (1962), 603–632.

J. F. Adams, On the groups J(X), IV, Topology 5 (1966), 21–71.

J. F. Adams and M. F. Atiyah, K–theory and the Hopf invariant, Quart. J. Math. 17 (1966), 31–38.

M. Atiyah and F. Hirzebruch, Vector BundlesMathworldPlanetmath and Homogeneous Spaces, Proc. Sym. Pure Math. III (1961), 7–38.

M. Atiyah, Vector bundles and the Künneth formulaMathworldPlanetmathPlanetmath, Topology 1 (1962), 245–248.

M. Atiyah, Power Operations in K–Theory, Quart. J. Math. Oxford. 17 (1966), 165–193.

M. Atiyah, K–Theory and reality, Quart. J. Math. Oxford. 17 (1966), 367–386.

M. Atiyah and R. Bott, On the periodicity theorem for complex vector bundles, Acta Math.112 (1964), 229–247.

M. Atiyah, R. Bott and A. Shapiro, Clifford Modules, Topology 3 (1964), 3–38.

R. Bott and J. Milnor, On the parallelizability of spheres, Bull. A.M.S. 64 (1958), 87–89.

R. Bott, The stable homotopyMathworldPlanetmathPlanetmath of the classical groupsMathworldPlanetmath, Ann. of Math. 70 (1959), 313–337.

A. Hatcher. Vector Bundles and K-TheoryMathworldPlanetmath. Web-book, 110 pages, May 2009.

L. Hodgkin, On the K–Theory of Lie groups, Topology. 6 (1967), 1–36.

M. Mahowald, The order of the image of the JhomomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath, Bull. A.M.S. 76 (1970), 1310–1313.

J. Milnor, Some consequences of a theorem of Bott, Ann. of Math. 68 (1958), 444–449.

D. Quillen, The Adams conjecture, Topology 10 (1971), 67–80.

D. Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. 100 (1974),1–79.

L. M. Woodward, Vector fields on spheres and a generalizationPlanetmathPlanetmath, Quart. J. Math. Oxford. 24 (1973), 357–366.

1.3 K–Theory MSC Classifications

18–XX Category theoryMathworldPlanetmathPlanetmathPlanetmathPlanetmath; homological algebra For commutative rings see 13Dxx, for associative rings
16Exx, for groups 20Jxx, for topological groups and related structuresMathworldPlanetmath 57Txx; see also 55Nxx and 55Uxx for algebraic topology
18Axx General theory of categoriesMathworldPlanetmath and functorsMathworldPlanetmath
18Fxx Categories and geometry
18F25 Algebraic K–theory and L–theory [See also 11Exx, 11R70, 11S70, 12-XX, 13D15, 14Cxx, 16E20, 19-XX, 46L80, 57R65, 57R67]
19–XX K–theory [See also 16E20, 18F25]

19Dxx Higher algebraic K–theory
19D10 Algebraic K-theory of spaces

19D25 Karoubi-Villamayor-Gersten K–theory

19D35 Negative K-theory, NK and Nil

19D45 Higher symbols, Milnor K–theory

19D50 Computations of higher K–theory of rings [See also 13D15, 16E20]

19D55 K-theory and homologyMathworldPlanetmathPlanetmath; cyclic homology and cohomologyMathworldPlanetmathPlanetmath [See also 18G60]

19Exx K–theory in geometry

19E08 K–theory of schemes [See also 14C35]

19Fxx K-theory in number theoryMathworldPlanetmath [See also 11R70, 11S70]

19F05 Generalized class field theory [See also 11G45]

19Gxx K-theory of forms [See also 11Exx]

19G24 L-theory of group ringsMathworldPlanetmath [See also 11E81]

19G38 Hermitian K-theory, relationsMathworldPlanetmathPlanetmathPlanetmath with K-theory of rings

19Kxx K-theory and operator algebras [See mainly 46L80, and also 46M20]

19K35 Kasparov theory (KK–theory) [See also 58J22]

19K56 Index theory [See also 58J20, 58J22]

19Lxx Topological K–theory [See also 55N15, 55R50, 55S25]

19L41 ConnectiveMathworldPlanetmath K–theory, cobordism [See also 55N22]

19L47 Equivariant K–theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91]

19L50 Twisted K-theory; differential K–theory

19Mxx Miscellaneous applications of K-theory

19M05 Miscellaneous applications of K-theory MSC Classification Search engine


Title bibliography for K-theory and vector bundles
Canonical name BibliographyForKtheoryAndVectorBundles
Date of creation 2013-03-22 19:31:18
Last modified on 2013-03-22 19:31:18
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 12
Author bci1 (20947)
Entry type Bibliography
Classification msc 11S70
Classification msc 11G45
Classification msc 19E08
Classification msc 18G60
Classification msc 18-00
Classification msc 19D55
Classification msc 57R67
Classification msc 57R65
Classification msc 46L80
Classification msc 14C35
Classification msc 46L80
Classification msc 16E20
Classification msc 18F25
Classification msc 11R70