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DTSTART:20131103T020000
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UID:calendar.7174.field_date.0@calendar.lafayette.edu
DTSTAMP:20260609T061414Z
DESCRIPTION:We consider two operations on the edge of an embedded (i.e. rib
 bon) graph: \ngiving a half-twist to the edge and taking the partial dual 
 with respect to \nthe edge.   These two operations give rise to an action 
 of  \, the ribbon \ngroup of G\,  on G.  We show that this ribbon group ac
 tion gives a complete \ncharacterization of duality in that if G is any ce
 llularly embedded graph \nwith medial graph Gm\, then the orbit of G under
  the group action is precisely \nthe set of all graphs with medial graphs 
 isomorphic (as abstract graphs) to \nGm .  We then show how this group act
 ion leads to a deeper understanding of \nthe properties of\, and relations
 hips among\, various graph polynomials such as \nthe generalized transitio
 n polynomial\, an extension of the Penrose polynomial \nto embedded graphs
 \, and the topological Tutte polynomials of Las Vergnas and \nalso Bollob\
 'as and Riordan\, as well as various knot and link invariants. We \nmake a
  brief excursion into a motivating application arising from emergent \nnan
 otechnology design strategies.  This is joint work with Iain Moffatt.
DTSTART;TZID=America/New_York:20130314T161500
DTEND;TZID=America/New_York:20130314T173000
LAST-MODIFIED:20130305T161951Z
LOCATION:Pardee 217
SUMMARY:Ribbon Graphs & Twisted Duality
URL;TYPE=URI:https://calendar.lafayette.edu/node/7174
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