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SUMMARY:Infinite-dimensional Morse indices and new invariants of G2-manifo
 lds - Laurence Mayther (Cambridge)
DTSTART:20231011T150000Z
DTEND:20231011T160000Z
UID:TALK206695@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:There are two main methods of constructing compact manifolds w
 ith holonomy G2\, viz. resolution of singularities (first applied by Joyce
 ) and twisted connect sum (first applied by Kovalev).  In the second case\
 , there is a known\, computable invariant (the \\nu-invariant\, introduced
  by Crowley–Goette–Nordström) which can be used to distinguish betwee
 n different examples. However no such invariant is known for the first con
 struction.\n\nIn this talk\, I will introduce two new invariants of G2-man
 ifolds\, termed \\mu-invariants\, and explain why these promise to be well
 -suited to\, and computable on\, Joyce's examples of G2-manifolds.  These 
 invariants are related to \\eta- and \\zeta-invariants and should be regar
 ded as the Morse indices of a G2-manifold when it is viewed as a critical 
 point of certain Hitchin functionals.  I shall also explain how to compute
  the \\mu-invariants in closed form on the orbifolds used in Joyce's const
 ruction\, using Epstein \\zeta-functions.
LOCATION:MR13
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