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SUMMARY:Heegaard Floer and Embedded Contact homology\, an introduction - T
 om Brown (DPMMS)
DTSTART:20170519T140000Z
DTEND:20170519T150000Z
UID:TALK71744@talks.cam.ac.uk
CONTACT:36916
DESCRIPTION:Heegaard Floer homology\, HF\, is a 3-manifold invariant defin
 ed combinatorially in terms of the Heegaard diagram for the manifold.  The
 re is also a version for knots in 3-manifolds called HFK.  Embedded contac
 t homology\, ECH\, is a dynamic invariant defined in terms of periodic orb
 its of the contact Reeb vector field\, and by controlling orbits near the 
 knot a knot version\, ECK\, can be obtained in this setting as well.  Coli
 n\, Ghiggini and Honda recently proved that the 3-manifold invariants HF a
 nd ECH are isomorphic\, and it is conjectured that HFK and ECK are isomorp
 hic.  With the help of pictures and examples\, I will talk about these two
  theories\, discuss their isomorphism and\, if time permits\, talk about m
 y research concerning a surgery formula in ECK analogous to a well-known f
 ormula on HFK.
LOCATION:MR13
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