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CATEGORIES:Lecture / Talk / Workshop
DESCRIPTION:Shawn Cui\, Purdue University\n\nAbstract: The Kuperberg invari
ant is a topological invariant of closed 3-manifolds based on finite-dimens
ional Hopf algebras. Here we initiate the program of constructing 4-manifo
ld invariants in the spirit of Kuperberg's 3-manifold invariant. We utilize
a structure called a Hopf triplet\, which consists of three Hopf algebras
and a bilinear form on each pair subject to certain compatibility condition
s. In our construction\, we present 4-manifolds by their trisection diagram
s\, a four-dimensional analog of Heegaard diagrams. The main result is that
every Hopf triplet yields a diffeomorphism invariant of closed 4-manifolds
. In special cases\, our invariant reduces to Crane-Yetter invariants and
generalized dichromatic invariants\, and conjecturally Kashaev's invariant.
As a starting point\, we assume that the Hopf algebras involved in the Ho
pf triplets are semisimple. We speculate that relaxing semisimplicity will
lead to even richer invariants.
DTEND:20210412T224500Z
DTSTAMP:20210621T032845Z
DTSTART:20210412T213000Z
LOCATION:
SEQUENCE:0
SUMMARY:Geometry\, Topology and Categorification Seminar: Trisection invari
ants of 4-manifolds from Hopf algebras
UID:tag:localist.com\,2008:EventInstance_36396045305708
URL:https://calendar.usc.edu/event/geometry_topology_and_categorification_s
eminar_trisection_invariants_of_4-manifolds_from_hopf_algebras
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