# 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. $Dieudonn\'{e}$, A History of Algebraic and Differential Topology 1900-1960, $Birkh\"{a}user$, 1989.

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

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

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

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

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 Bundles and Homogeneous Spaces, Proc. Sym. Pure Math. III (1961), 7–38.

M. Atiyah, Vector bundles and the Künneth formula, 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 homotopy of the classical groups, Ann. of Math. 70 (1959), 313–337.

A. Hatcher. Vector Bundles and K-Theory. Web-book, 110 pages, May 2009. $http://aux.pp-dev.org:8080/files/books/413/VBKtheoryHatcher.pdf$

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

M. Mahowald, The order of the image of the $J$homomorphism, 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 generalization, Quart. J. Math. Oxford. 24 (1973), 357–366.

### 1.3 K–Theory MSC Classifications

18–XX Category theory; homological algebra For commutative rings see 13Dxx, for associative rings
16Exx, for groups 20Jxx, for topological groups and related structures 57Txx; see also 55Nxx and 55Uxx for algebraic topology
18Axx General theory of categories and functors
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 homology; cyclic homology and cohomology [See also 18G60]

19Exx $K$–theory in geometry

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

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

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

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

19G38 Hermitian $K$-theory, relations 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]

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

19L41 Connective $K$–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

$http://www.ams.org/mathscinet/msc/msc2010.html?t=&s=K-theory&btn=Search&ls=s$

http://www.ams.org/mathscinet/msc/msc2010.htmlAMS MSC Classification Search engine

$11Exx,11R70,11S70,12-XX,13D15,14Cxx,16E20,19-XX,46L80,57R65,57R67$

 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