## Math 583 - Possible Project Papers

Please select a paper, and tell me which one you’ve selected, before Sunday March 17. For guidance, click on the titles to go to MathSciNet reviews of the papers, or chat with me.

You’re very welcome to suggest a paper that is

After you’ve chosen your paper, your job is to prepare an approximately five-page typed report that explains or introduces the paper to persons with the background provided by our class. Rigorous proofs are not required; your job is to produce something that would be of value to others in the class.

Thanks, and good luck!

Atiyah - 1962 - Vector bundles and the Künneth formula

Atiyah - 1966 - K-theory and reality

Atiyah, Hirzebruch - 1961 - Bott periodicity and the parallelizability of the spheres

Bott - 1959 - The stable homotopy of the classical groups. See also Milnor - Morse theory

Segal - 1968 - Equivariant K-theory

Kuiper - 1965 - The homotopy type of the unitary group of Hilbert space and Cuntz, Higson - 1987 - Kuiper’s theorem for Hilbert modules

Atiyah - The space of Fredholm operators (Appendix to the book

Atiyah, Singer - 1969 - Index theory for skew-adjoint Fredholm operators

Atiyah - 1969 - Algebraic topology and operators in Hilbert space

Atiyah - 1968 - Bott periodicity and the index of elliptic operators

Atiyah, Segal - 1969 - Equivariant K-theory and completion

Atiyah - 1971 - Riemann surfaces and spin structures

Pimsner, Voiculescu - 1982 -K-groups of reduced crossed products by free groups

Cuntz - 1981 - K-theory for certain C*-algebras

You’re very welcome to suggest a paper that is

*not*on the list below. But please get my approval of your choice before March 17.

After you’ve chosen your paper, your job is to prepare an approximately five-page typed report that explains or introduces the paper to persons with the background provided by our class. Rigorous proofs are not required; your job is to produce something that would be of value to others in the class.

Thanks, and good luck!

Atiyah - 1962 - Vector bundles and the Künneth formula

Atiyah - 1966 - K-theory and reality

Atiyah, Hirzebruch - 1961 - Bott periodicity and the parallelizability of the spheres

Bott - 1959 - The stable homotopy of the classical groups. See also Milnor - Morse theory

Segal - 1968 - Equivariant K-theory

Kuiper - 1965 - The homotopy type of the unitary group of Hilbert space and Cuntz, Higson - 1987 - Kuiper’s theorem for Hilbert modules

Atiyah - The space of Fredholm operators (Appendix to the book

*K-Theory*)Atiyah, Singer - 1969 - Index theory for skew-adjoint Fredholm operators

Atiyah - 1969 - Algebraic topology and operators in Hilbert space

Atiyah - 1968 - Bott periodicity and the index of elliptic operators

Atiyah, Segal - 1969 - Equivariant K-theory and completion

Atiyah - 1971 - Riemann surfaces and spin structures

Pimsner, Voiculescu - 1982 -K-groups of reduced crossed products by free groups

Cuntz - 1981 - K-theory for certain C*-algebras