November 16, David Wärn, Path spaces of pushouts via a zigzag construction

[Dan Christensen]

The next HoTTEST seminar is on Thursday, November 16 at 11:30am EST
(UTC-5) = 16:30 UTC. Summer time has ended in the US and Canada, so
we're back in sync with Europe.

David Wärn will be speaking about "Path spaces of pushouts via a zigzag
construction". The talk will be 60 minutes long, followed by up to 30
minutes of discussion. 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 available at:

https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html

Dan

(On behalf of the HoTTEST organizers: Carlo Angiuli, Dan Christensen,
Chris Kapulkin, and Emily Riehl.)

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David Wärn

Path spaces of pushouts via a zigzag construction

Working in informal HoTT, we introduce the zigzag construction to
describe path spaces of arbitrary pushouts as sequential colimits of
pushouts. The construction is no more complicated than the James
construction but much more general. By analysing this construction, we
obtain direct proofs of the Blakers–Massey theorem, various results in
combinatorial group theory, and the fact that any pushout of 0-types is
a 1-type. The lattermost resolves an open problem in HoTT mentioned
already in the HoTT book. While this talk will assume some familiarity
with HoTT, the construction may be of interest to topologists more
generally.