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SUMMARY:Roger Picken (Instituto Superior Técnico\, Lisbon)
DTSTART:20210409T160000Z
DTEND:20210409T170000Z
DTSTAMP:20260423T021421Z
UID:TQFT/35
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TQFT/35/">Li
 nk invariants from finite crossed modules and a lifting of the Eisermann i
 nvariant</a>\nby Roger Picken (Instituto Superior Técnico\, Lisbon) as pa
 rt of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbstract\n
 This talk is based on work with João Faria Martins (Univ. Leeds) [1] and 
 several projects with students. I will describe the construction of an inv
 ariant of tangles and framed tangles which takes values in an arbitrary cr
 ossed module of finite groups. This involves the fundamental crossed modul
 e associated to a natural topological pair coming from a knot diagram\, an
 d a suitable class of morphisms from this fundamental crossed module to th
 e chosen finite crossed module. Our construction includes all rack and qua
 ndle cohomology (framed) link invariants\, as well as the Eisermann invari
 ant of knots [2-3]\, for which we also find a lifting. The Eisermann invar
 iant detects information about a suitable choice of meridian and longitude
  in the knot complement boundary.\n\n<p>[1] João Faria Martins and Roger 
 Picken: Link invariants from finite categorical groups\, Homology\, Homoto
 py and Applications\, 17(2) (2015)\, 205–233\; <a href="https://arxiv.or
 g/abs/1301.3803">arXiv:1301.3803v2</a> [math.GT]\, <a href="https://arxiv.
 org/abs/1612.03501">arXiv:1612.03501v1</a> [math.GT]<br />\n[2] M. Eiserma
 nn: Knot colouring polynomials\, Pacific J. Math. 231 (2007)\, no. 2\, 305
 –336.<br />\n[3] M. Eisermann: Homological characterization of the unkno
 t\, J. Pure Appl. Algebra 177 (2003)\, no. 2\, 131–157.</p>\n
LOCATION:https://researchseminars.org/talk/TQFT/35/
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