Markus Hausmann: Formal groups in algebraic topology
Time: Wed 2022-03-16 13.15 - 14.15
Participating: Markus Hausmann (SU)
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".
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