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CATEGORIES:Category Theory Seminar
SUMMARY:Magnitude homology - Tom Leinster (University of E
dinburgh)
DTSTART;TZID=Europe/London:20170530T141500
DTEND;TZID=Europe/London:20170530T151500
UID:TALK71947AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/71947
DESCRIPTION:Magnitude homology is a homology theory of enriche
d categories\, proposed by Michael Shulman late la
st year. For ordinary categories\, it is the usua
l homology of a category (or equivalently\, of its
classifying space). But for metric spaces\, rega
rded as enriched categories à la Lawvere\, magnitu
de homology is something new. It gives truly metr
ic information: for instance\, the first homology
of a subset X of R^n detects whether X is convex.\
n\nLike all homology theories\, magnitude homology
has an Euler characteristic\, defined as the alte
rnating sum of the ranks of the homology groups.
Often this sum diverges\, so we have to use some f
ormal trickery to evaluate it. In this way\, we en
d up with an Euler characteristic that is often no
t an integer. This number is called the "magnitud
e" of the enriched category. In topological settin
gs it is the ordinary Euler characteristic\, and i
n metric settings it is closely related to volume\
, surface area and other classical invariants of g
eometry.
LOCATION:MR5\, Centre for Mathematical Sciences
CONTACT:Tamara von Glehn
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