reply to r.brown@bangor.ac.uk The paper (with O. MUCUK), ``The monodromy groupoid of a Lie groupoid'', {\em Cah. Top. G\'eom. Diff. Cat},36 (1995) 345-369. develops work of Pradines (1966) to define a monodromy groupoid of a Lie groupoid precisely as the Lie groupoid for extendibility of local morphisms (monodromy principle), and relates this to the construction of a Lie groupoid as the union of the universal covers of the stars of a given Lie groupoid. These ideas are also developed to the local subgroupoid case in (with \.I. \.I\c cen ), 'Locally Lie subgroupoids and their Lie holonomy and monodromy groupoids', {\it Top. and its Appl.} 115 (2001) 125-138. and given an exposition in (with I.ICEN and O. MUCUK) `Holonomy and monodromy groupoids', in Lie Algebroids, Banach Center Publications, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 54 (2001) 9-20. math.CT/0008117 Following Pradines, the Lie structure on the monodromy groupoid is obtained via a holonomy construction: (with M. E.-S. A.-F. AOF), ``The holonomy groupoid of a locally topological groupoid'', {\em Top. and its Appl.}, 47 (1992) 97-113. This generalises the holonomy groupoid of a foliation. Note that the groupoids used in Connes' book are equivalence relations and holonomy groupoids of foliations. (Please inform me if I am wrong on this.) How to link the above work with Algebraic Quantum Field Theory, is another matter. Information welcomed! Ronnie Brown ----- Original Message ----- From: "James Stasheff" <jds@math.upenn.edu> To: <categories@mta.ca> Sent: Sunday, July 07, 2002 1:47 PM
A student asks:
I heard that Monodromy is a general concept in category theory involving the globalization of local morphism. In Algebraic Quantum Field Theory, i.e. operator algebras in QFT, local morphism are the main stay,i.e. O-->R(O).
Do you know of any Intro. to Monodromy/Holonomy text I can begin from?, I'm at the level of Mac Lane's "Categories for the working Mathematican" 1998 and Mac Lane, Moerdijk "Sheaves in geometry and logic. A first into to Topos Theory" 1992.
Thanks
Jim Stasheff jds@math.upenn.edu
Home page: www.math.unc.edu/Faculty/jds
As of July 1, 2002, I am Professor Emeritus at UNC and I will be visiting U Penn but for hard copy the relevant address is: 146 Woodland Dr Lansdale PA 19446 (215)822-6707