{"id":2016,"date":"2021-04-21T11:20:47","date_gmt":"2021-04-21T08:20:47","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2016"},"modified":"2021-09-12T13:09:22","modified_gmt":"2021-09-12T10:09:22","slug":"online-seminar-u-haifa-topology-geometry-seminar-on-april-25-2021","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2016","title":{"rendered":"Online seminar, U. Haifa Topology & Geometry seminar on April 25, 2021"},"content":{"rendered":"\n

A recording of the talk is available here<\/a>.<\/p>\n\n\n\n

Topology & Geometry Seminar<\/u><\/strong><\/p>\n\n\n\n

Speaker: Nir Gadish, MIT<\/p>\n\n\n\n

Topic: M\u00f6bius inversion in homotopy theory<\/p>\n\n\n\n

Place: This is an online seminar. Please email David Blanc “blanc at math dot haifa dot ac dot il” for the Zoom ID and password.<\/p>\n\n\n\n

Time: 16:00<\/p>\n\n\n\n

Date: Sunday, April 25, 2021<\/p>\n\n\n\n

                                                   Abstract<\/u><\/strong>:<\/u><\/strong><\/p>\n\n\n\n

M\u00f6bius inversion is classically a procedure in number theory that inverts summation of functions over the divisors of an integer. A similar construction is possible for every locally finite poset, and is governed by a so called M\u00f6bius function encoding the combinatorics. In 1936 Hall observed that the values of the M\u00f6bius function are Euler characteristics of intervals in the poset, suggesting a homotopy theoretic context for the inversion.
In this talk we will discuss a functorial ‘space-level’ realization of M\u00f6bius inversion for diagrams taking values in any pointed cocomplete infinity-category. The role of the M\u00f6bius function will be played by h\u00f6motopy types whose reduced Euler characteristics are the classical values, and inversion will hold up to extensions (think inclusion-exclusion but with the alternating signs replaced by even\/odd spheres).
This provides a uniform perspective to many constructions in topology and algebra. Notable examples that I hope to mention include handle decompositions, Koszul resolutions, and filtrations of configuration spaces.<\/p>\n","protected":false},"excerpt":{"rendered":"

A recording of the talk is available here. Topology & Geometry Seminar Speaker: Nir Gadish, MIT Topic: M\u00f6bius inversion in homotopy theory Place: This is an online seminar. Please email David Blanc “blanc at math dot haifa dot ac dot il” for the…
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