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1-2-3 Seminar: What is a cohomology operation?

Alex Waugh, University of Washington
Friday, May 10, 2024 - 2:30pm to 3:30pm
PDL C-401

In a first course in algebraic topology, one is often introduced to the cup product as a means of strengthening cohomology as an invariant. That is, two spaces may have the same cohomology groups, but fail to have the same cohomology rings (and are therefore not homotopy equivalent). One can ask if there is a further refinement of cohomology which can be used to distinguish spaces which have the same cohomology rings, but are not homotopy equivalent. We will motivate such a refinement via examples leading to "stable cohomology operations". Finally, we will use these operations to show that \pi_4(S^3) is nontrivial.

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