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SUMMARY:Pictures and Picture Groups\, Lecture II\, More on Picture Groups 
 for Valued Quivers &amp\; Cubical Structures of Cluster Morphism Categorie
 s - Gordana Todorov (Northeastern University)
DTSTART:20211124T150000Z
DTEND:20211124T160000Z
UID:TALK165232@talks.cam.ac.uk
DESCRIPTION:\n\n\nPart 1: Let Q be a valued quiver. We already defined the
  picture LQ and the picture group G0(LQ). I will point out a few more fact
 s about semi-invariant pictures and picture groups for valued (and modulat
 ed) quivers. This was in- spired by Tomoki Nakanishi&rsquo\;s comment abou
 t picture groups for valued quivers.\nPart 2: The original motivation for 
 introducing Cluster Morphism Categories was to obtain cubical categories (
 with an additional structure &ldquo\;locally CAT(0)&rdquo\;) which was use
 d to prove that the picture space is a K(&pi\;\, 1) for the picture group\
 , which was an important step for computing homology of picture groups. Th
 e notion of Cluster Morphism Category was beautifully generalized by Aslak
  Buan and Bethany Marsh and we already heard their talks. Also\, Eric Hans
 on showed that the Picture space for Nakayama algebras is a K(&pi\;\,1). I
 t would be good to know which of the spaces are K(&pi\;\,1) for Picture gr
 oups of algebras which are not hereditary of finite type.\n\n\n
LOCATION:Seminar Room 2\, Newton Institute
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