Steenrod operations via higher Bruhat orders

Abstract: The cohomology of a topological space has a ring structure via the cup product. The cup product is defined at the level of cochains, where it is not commutative, but it becomes commutative at the cohomology level. At the cochain level, the lack of commutativity is resolved homotopically by an infinite tower of higher products, known as the Steenrod cup-i products. This additional structure provides more refined information which can be used to tell apart non-homotopy-equivalent spaces. In this talk, I will explain recent work with Guillaume Laplante-Anfossi, where we show how conceptual proofs of the key properties of Steenrod's cup-i products can be given using the higher Bruhat orders of Manin and Schechtman.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: https://uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09

Meeting ID: 918 7552 8987 Password: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.

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