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SUMMARY:Critical points of low index for the systole function - Maxime For
 tier-Bourque\, Glasgow
DTSTART:20190130T160000Z
DTEND:20190130T170000Z
UID:TALK114862@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:The systole of a hyperbolic surface is the length of any of it
 s shortest geodesics. Akrout showed that this defines a topological Morse 
 function on the Teichmuller space of the surface. As such\, the critical p
 oints of the systole function carry information about the topology of modu
 li space. Schmutz Schaller found a critical point of index 2g-1 in every g
 enus g>1 and conjectured that this was the smallest index possible\, becau
 se of the virtual cohomological dimension of moduli space calculated by Ha
 rer. I will describe a family of counterexamples: for every c>0\, there ex
 ists a closed hyperbolic surface of genus g which is a critical point of i
 ndex at most cg.
LOCATION:MR13
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