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SUMMARY:Lvzhou Chen (University of Texas-Austin)
DTSTART:20200922T150000Z
DTEND:20200922T160000Z
DTSTAMP:20260423T004038Z
UID:OSUGGT/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSUGGT/9/">S
 table commutator lengths of integral chains in right-angled Artin groups</
 a>\nby Lvzhou Chen (University of Texas-Austin) as part of Ohio State Topo
 logy and Geometric Group Theory Seminar\n\n\nAbstract\nIt follows from the
 orems of Agol and Kahn-Markovic that the fundamental group of any closed h
 yperbolic 3-manifold contains a special subgroup of finite index. Very lit
 tle is known about how large the index needs to be. Motivated by this\, in
  this joint work with Nicolaus Heuer\, we study stable commutator lengths 
 (scl) of integral chains in right-angled Artin groups (RAAGs). Topological
 ly\, an integral 1-chain in a group G is a collection of loops in the K(G\
 ,1) space with integral weights\, and its scl is the least complexity of s
 urfaces bounding the weighted loops. We show that the infimal positive scl
  of integral chains in any RAAG is positive\, and its size explicitly depe
 nds on the defining graph of the RAAG up to a multiplicative constant 12. 
 In particular\, the size is non-uniform among RAAGs\, which is unexpected.
 \n
LOCATION:https://researchseminars.org/talk/OSUGGT/9/
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