Quillen Seminar, Spring 2006

LOW 115, Monday 4:30-5:30pm

Some references

Principal Reference:
  • D. Quillen, The spectrum of an equivariant cohomology ring, I, II Ann. Math. 94 (1971), 549-572, 573-602. For more algebraically oriented treatment (finite groups only):
  • D. Quillen, B. B. Venkov, Cohomology of finite groups and elementary abelian subgroups. Topology 11 (1972), 317--318. Group cohomology:
  • K. Brown, Cohomology of groups, Springer, NY, (1982)
  • L. Evens, The cohomology of groups, Oxford University Press, (1991)
  • C. A. Weibel, An Introduction to Homological Algebra, Cambridge Studies in Adv. Math. 38, Cambridge Univ.Press, Cambridge, (1994). Equivariant cohomology:
  • D.J.Benson, Representations and cohomology, Volume II, Cambridge University Press, 1991. More computational references:
  • D. Quillen, The mod 2 cohomology rings of extra-special 2-groups and the spinor groups, Math. Ann. 194 (1971) 197--212.
  • A. Adem, R. J. Milgram, Cohomology of finite groups, Springer, (1994)

    Notes by Steve Mitchell

  • Principal bundles and Classifying spaces
  • Quillen's work on the Atiyah-Swan conjecture

    Bits of schedule

  • April, 3. Steve Mitchell: Introductory/overview lecture
  • April, 10. Luke Gutzwiller: Finite generation of the cohomology algebra: topological proof
  • April, 17. Alex Papazoglou: Finite generation of the cohomology algebra: algebraic proof
    Hand-out: "Evens' Norm and Finite generation of Group Cohomology".
  • April, 24. Dave Rosoff: Borel Construction, Atiyah-Swan conjecture and detection of nilpotent in cohomology (Theorems A and C in Steve Mithcel's notes)
  • May, 1 - International Labor Day! Anton Dochtermann: Minimal prime ideals of $H^*(G)$ via an approximation to equivariant cohomology
  • May, 8. Anton Dochtermann: Theorems A,B and C for equivariant cohomology from the $F$-isomorphism theorem
    Eliana Hechter: Examples
  • May 15. Troy Winfree: Proof of the F-isomorphism theorem
  • May 22. Julia Pevtsova: Finally, the stratification Theorem