December 14: David Jaz Myers, The Tangent Bundle of Spheres
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Emily Riehl
Dec 13, 2023, 7:36:14 AM12/13/23
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The HoTTEST seminar continues this Thursday at the usual (winter) time, 11:30am EST = 16:30 UTC.
Our speaker is David Jaz Myers, whose talk is titled "The Tangent Bundles of Spheres". The talk will be 60 minutes long, followed by
up to 30 minutes for questions. The abstract is below.
The Zoom link is https://zoom.us/j/994874377
Further information, including the list of upcoming speakers, and videos and slides from past talks, is at:
https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html
Emily
(On behalf of the HoTTEST organizers: Carlo Angiuli, Dan Christensen, Chris Kapulkin, and Emily Riehl.)
Title: The Tangent Bundles of Spheres
jww Ulrik Buchholtz, Dan Christensen, and Egbert Rijke
Abstract:
In this talk, we'll construct the tangent sphere bundles on the spheres using an inductive construction, and we'll use this construction to prove the Hairy Ball Theorem. We'll then compute the Euler class of the tangent sphere bundles with an explicit construction. Generalizing from this case, we'll define a preliminary notion of "homotopy manifold" and use an abstract lemma about pushout products to define the product of homotopy manifold structures. This will give us tangent bundles on products of spheres as well. All of this will take place in ordinary book HoTT, and a good deal of it has already been formalized in Coq.
--
Professor of Mathematics (she/her)
Johns Hopkins University
emilyriehl.github.io
Our speaker is David Jaz Myers, whose talk is titled "The Tangent Bundles of Spheres". The talk will be 60 minutes long, followed by
up to 30 minutes for questions. The abstract is below.
The Zoom link is https://zoom.us/j/994874377
Further information, including the list of upcoming speakers, and videos and slides from past talks, is at:
https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html
Emily
(On behalf of the HoTTEST organizers: Carlo Angiuli, Dan Christensen, Chris Kapulkin, and Emily Riehl.)
Title: The Tangent Bundles of Spheres
jww Ulrik Buchholtz, Dan Christensen, and Egbert Rijke
Abstract:
In this talk, we'll construct the tangent sphere bundles on the spheres using an inductive construction, and we'll use this construction to prove the Hairy Ball Theorem. We'll then compute the Euler class of the tangent sphere bundles with an explicit construction. Generalizing from this case, we'll define a preliminary notion of "homotopy manifold" and use an abstract lemma about pushout products to define the product of homotopy manifold structures. This will give us tangent bundles on products of spheres as well. All of this will take place in ordinary book HoTT, and a good deal of it has already been formalized in Coq.
--
Professor of Mathematics (she/her)
Johns Hopkins University
emilyriehl.github.io
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