bibliography for K-theory and vector bundles

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.

D

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i

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e

⁢

u

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d

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o

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n

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n

⁢

é

, A History of

Algebraic

and Differential Topology 1900-1960,

B

⁢

i

⁢

r

⁢

k

⁢

h

⁢

ä

⁢

u

⁢

s

⁢

e

⁢

r

, 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.

S. Lang,

Algebra

, 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 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.

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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]

19F05 Generalized

class field theory

[See also 11G45]

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 (

K

⁢

K

–theory) [See also 58J22]

19K56

Index theory

[See also 58J20, 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

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http://www.ams.org/mathscinet/msc/msc2010.html

AMS MSC Classification Search engine

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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

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