The works collected in this volume are based on the talks at the Manchester
Meeting of the London Mathematical Society, 6 July 2001, followed by an LMS-
sponsored international workshop, 7-13 July 2001, the topic and title of which
Quantization, deformations, and new homological and categorical methods in
Some of the papers are very close accounts of the actual
talks; others present new results developing those communicated at the meetings.
The papers are centered on the following topics: quantization in various aspects,
Poisson brackets and structures "beyond", - symplectic supermanifolds, operads,
Lie groupoids and Lie (bi)algebroids, algebras with n-ary operations, - to name
a few. I have tried to group the papers logically, at least as far as is practical.
The style of exposition varies. Some papers ar:e mainly addressed to experts, while
others can also serve as an accessible introduction and as reference texts. Hopefully,
this volume will be useful to a broad reading audience of researchers in geometry,
topology, algebra and mathematical physics.
ACKNOWLEDGEMENTS. There are several people and organizations that I would
like to thank. In 2001 the London Mathematical Society started its regional meet-
ings, of which the Manchester Meeting was one of the first. I thank the Society for
the help in organization and for the financial support of the Meeting and workshop.
The American Mathematical Society suggested to publish the proceedings, to which
the LMS kindly gave its blessing. I want to thank Sergei Gelfand for the idea of
this publication. Mike Prest and myself were the co-organizers of the meeting and
workshop, Mike often taking the harder part of the task. I am very grateful to
him. Thanks are due to UMIST (the University of Manchester Institute of Science
and Technology) for providing conference facilities and various help. The greatest
thanks are due to all the participants and especially to those who contributed to
these proceedings. Many friends and colleagues helped me during the work on the
book. I want to thank Alan Weinstein, Dmitry Gurevich, Alexander Karabegov,
Dmitry Roytenberg and Jens Hoppe. Special thanks go to Kirill Mackenzie and
John Rawnsley for crucial help, particularly at the final stages of the work.
Manchester, September 2002