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Markus Hausmann: Formal groups in algebraic topology

Time: Wed 2022-03-16 13.15 - 14.15

Location: Zoom, meeting ID: 694 6016 6420 (password required)

Lecturer: Markus Hausmann (SU)

Abstract:

A (1-dimensional, commutative) formal group law is a power series in two variables satisfying associativity, unitality and commutativity conditions, motivated by the properties of the formal completions of 1-dimensional algebraic groups at their identity element. Topologically, formal group laws arise from cohomology theories with Thom isomorphisms for complex vector bundles, such as ordinary cohomology or complex K-theory. This connection has been very fruitful and allows to explain many structural phenomena in stable homotopy theory.

In my talk I will first survey this relationship. I will then discuss how the study of cohomology theories on orbispaces/stacks gives rise to a decompleted version of this story, incorporating the algebraic groups themselves (rather than their formal completions) as well as a more general form of decompletion of formal groups called "global groups".

Note: The passcode was sent to the AG and NT mailing lists. If you're not on these lists and would like to attend, or are having trouble accessing the meeting, please email Wushi Goldring at wgoldring@math.su.se . To be added to the AG mailing list, please email Jonas Bergström at jonasb@math.su.se .