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SUMMARY:Infinitely presented simple groups separated by homological finite
 ness properties - Eduard Schesler (Karlsruhe Institute of Technology (KIT)
 )
DTSTART:20251001T100000Z
DTEND:20251001T110000Z
UID:TALK236176@talks.cam.ac.uk
DESCRIPTION:Given a finitely generated linear group $G$ over $\\mathbb{Q}$
 \, we construct a simple group $\\Gamma$ that has the same finiteness prop
 erties as $G$ and admits $G$ as a quasi-retract. As an application\, we co
 nstruct a simple group of type $FP_{\\infty}$ that is not finitely present
 ed. Moreover we show that for every $n \\in \\mathbb{N}$ there is a simple
  group of type $FP_n$ that is neither finitely presented nor of type $FP_{
 n+1}$. To prove these results we construct a self-similar version of the B
 estvina-Brady groups\, which allows us to apply the so-called R\\"over--Ne
 krashevich construction to them. In particular\, we obtain the first examp
 les of infinitely presented groups of type $FP_2$ that live in the world o
 f Thompson-like groups. This is joint work with&nbsp\;Claudio Llosa Isenri
 ch and&nbsp\;Xiaolei Wu.
LOCATION:Seminar Room 2\, Newton Institute
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