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SUMMARY:Fiona Torzewska (University of Bristol)
DTSTART:20240201T100000Z
DTEND:20240201T110000Z
DTSTAMP:20260423T035635Z
UID:EQuAL/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EQuAL/20/">T
 opological quantum field theories and homotopy cobordisms</a>\nby Fiona To
 rzewska (University of Bristol) as part of European Quantum Algebra Lectur
 es (EQuAL)\n\n\nAbstract\nI will begin by explaining the construction of a
  category CofCos\, whose objects are topological spaces and whose morphism
 s are cofibrant cospans. Here the identity cospan is chosen to be of the f
 orm $X\\to X\\times [0\,1]\\rightarrow X$\, in contrast with the usual ide
 ntity in the bicategory $Cosp(V)$ of cospans over a category $V$. The cate
 gory $CofCos$ has a subcategory $HomCob$ in which all spaces are homotopic
 ally 1-finitely generated. There exist functors into HomCob from a number 
 of categorical constructions which are potentially of use for modelling pa
 rticle trajectories in topological phases of matter: embedded cobordism ca
 tegories and motion groupoids for example. Thus\, functors from HomCob int
 o Vect give representations of the aforementioned categories.\n\nI will al
 so construct a family of functors $Z_G\\colon HomCob\\to Vect$\, one for e
 ach finite group $G$\, and show that topological quantum field theories pr
 eviously constructed by Yetter\, and an untwisted version of Dijkgraaf-Wit
 ten\, generalise to functors from HomCob. I will construct this functor in
  such a way that it is clear the images are finite dimensional vector spac
 es\, and the functor is explicitly calculable. I will also give example ca
 lculations throughout.\n
LOCATION:https://researchseminars.org/talk/EQuAL/20/
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