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SUMMARY:Lucia Martin Merchan (University of Waterloo)
DTSTART:20230222T220000Z
DTEND:20230222T230000Z
DTSTAMP:20260423T021232Z
UID:VSGS/64
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VSGS/64/">To
 pological properties of closed $\\mathrm{G}_2$ manifolds through compact q
 uotients of Lie groups</a>\nby Lucia Martin Merchan (University of Waterlo
 o) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nA
  $\\mathrm{G}_2$ structure on a 7-dimensional Riemannian manifold $(M\,g)$
  is determined by a stable of 3-form $\\varphi$. It is said to be closed i
 f $d\\varphi=0$ and torsion-free if $\\varphi$ is parallel. The purpose of
  this talk is to discuss two problems where compact quotients of Lie group
 s are useful for understanding topological properties of compact closed $\
 \mathrm{G}_2$ manifolds that don´t admit any torsion-free $\\mathrm{G}_2$
  structure. More precisely\, these problems are related to the open questi
 ons: Are simply connected compact closed $\\mathrm{G}_2$ manifolds almost 
 formal? Could a compact closed $\\mathrm{G}_2$ manifold have third Betti n
 umber $b_3=0$?\n\nUsing compact quotients of Lie groups\, we first outline
  the construction of a manifold admitting a closed $\\mathrm{G}_2$ structu
 re that is not almost formal and has first Betti number $b_1=1$. Later\, w
 e show that there aren´t invariant exact $\\mathrm{G}_2$ structures on co
 mpact quotients of Lie groups. The last result is joint work with Anna Fin
 o and Alberto Raffero.\n
LOCATION:https://researchseminars.org/talk/VSGS/64/
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