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SUMMARY:The surface category and tropical curves - Jan Steinebrunner\, Uni
 versity of Cambridge
DTSTART:20220202T160000Z
DTEND:20220202T170000Z
UID:TALK167471@talks.cam.ac.uk
CONTACT:Henry Wilton
DESCRIPTION:This talk will discuss the (truncated) surface category Cob_2 
 in which morphisms are diffeomorphism classes of surfaces and composition 
 is defined by gluing along boundaries. This is a simplified version of the
  topological bordism categories that have become a key tool for studying t
 he algebraic topology of diffeomorphism groups.\n\nWhat makes Cob_2 simple
 r is that it does not have moduli spaces built in: it only knows about the
  combinatorics of how surfaces glue up to diffeomorphism. Nevertheless\, I
  will show that the classifying space of a certain subcategory of Cob_2 ha
 s a surprisingly rich structure: it is splits off free infinite loop space
 s on the moduli stacks of tropical curves of arbitrary genus. The splittin
 g map admits a nice pictorial description.\n\nIf time permits\, I will als
 o speculate on how one might use Cob_2 to study the unstable homology of M
 _g.
LOCATION:MR13
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