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      k-theory learning seminar

organized by myself and Jacob Gaiter

tuesdays at 11 in pma 9.166

mailing list: k-theory@utlists.utexas.edu

      schedule

week 1 (8/29): review of vector bundles, clutching, and grassmanians (Jacob, notes)

week 2 (9/5): grothendieck completion and K^0 (Abhishek S, notes)

week 3 (9/12): K(X) and the fundamental product theorem (Isaac, notes)

week 4 (9/19): higher K groups and cohomology (Aru, notes)

week 5 (9/26): Bott periodicity I (Abhishek K)

week 6 (10/3): bye week

week 7 (10/10): division algebras and parallelizable spheres (Cas, notes)

week 8 (10/17): vector fields on spheres (Jayden)

week 9 (10/24): the Atiyah-Singer index theorem I: pseudo-differential operators (Justin, notes)

week 10 (10/31): bye week

week 11 (11/7): the Atiyah-Singer index theorem II: Chern, Thom, et al. (Abhishek S, notes)

week 12 (11/14): the Atiyah-Singer index theorem III: the grand finale (Jacob, notes)

      sources

k-theory by Karoubi

k-theory by Atiyah

vector bundles and k-theory by Hatcher, a good resource but unfinished

topological k-theory and some of its applications, Saad Slaoui's master's thesis

a geometric introduction to k-theory, includes both topological and algebraic k-theory

Dan Freed's k-theory class, includes potentially useful lecture notes and lots of sources for further reading

k-theory and elliptic operators, expository notes on the k-theoretic formulation and proof of the Atiyah-Singer index theorem