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Please note this event occurred in the past.
April 12, 2024 2:30 pm - 2:30 pm ET
Geometry and Topology Seminar
LGRT 1681

Cohen famously showed that as an operad the homology of the collection of ordered configuration spaces Conf(ℝn,βˆ’)Conf(𝑅𝑛,βˆ’) is generated by

Hβˆ—(Conf(ℝn,2))=Hβˆ—(Snβˆ’1)=β„€βŸ¨(βˆ’β‹…βˆ’),[βˆ’,βˆ’]⟩,π»βˆ—(Conf(𝑅𝑛,2))=π»βˆ—(π‘†π‘›βˆ’1)=π‘βŸ¨(βˆ’β‹…βˆ’),[βˆ’,βˆ’]⟩,

and the formal symbols (βˆ’β‹…βˆ’),[βˆ’,βˆ’](βˆ’β‹…βˆ’),[βˆ’,βˆ’] are subject precisely to the relations defining n𝑛-Poisson algebras. We discuss a generalization of this to the ordered configuration spaces of an arbitrary framed manifold. The result is a spectral sequence computing Hβˆ—(Conf(M,βˆ’))π»βˆ—(Conf(𝑀,βˆ’)). This spectral sequence looks surprisingly similar to the Goodwillie spectral sequence which for a simply connected space X𝑋 converges to Ο€βˆ—(X)πœ‹βˆ—(𝑋).