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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:The surface category and tropical curves - Jan Ste
inebrunner\, University of Cambridge
DTSTART;TZID=Europe/London:20220202T160000
DTEND;TZID=Europe/London:20220202T170000
UID:TALK167471AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/167471
DESCRIPTION:This talk will discuss the (truncated) surface cat
egory Cob_2 in which morphisms are diffeomorphism
classes of surfaces and composition is defined by
gluing along boundaries. This is a simplified vers
ion of the topological bordism categories that hav
e become a key tool for studying the algebraic top
ology of diffeomorphism groups.\n\nWhat makes Cob_
2 simpler is that it does not have moduli spaces b
uilt in: it only knows about the combinatorics of
how surfaces glue up to diffeomorphism. Neverthele
ss\, I will show that the classifying space of a c
ertain subcategory of Cob_2 has a surprisingly ric
h structure: it is splits off free infinite loop s
paces on the moduli stacks of tropical curves of a
rbitrary genus. The splitting map admits a nice pi
ctorial description.\n\nIf time permits\, I will a
lso speculate on how one might use Cob_2 to study
the unstable homology of M_g.
LOCATION:MR13
CONTACT:Henry Wilton
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