Volume 11, issue 2 (2011)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Differential operators and the wheels power series

Andrew Kricker

Algebraic & Geometric Topology 11 (2011) 1107–1162
Abstract

An earlier work of the author’s showed that it was possible to adapt the Alekseev–Meinrenken Chern–Weil proof of the Duflo isomorphism to obtain a completely combinatorial proof of the wheeling isomorphism. That work depended on a certain combinatorial identity, which said that a particular composition of elementary combinatorial operations arising from the proof was precisely the wheeling operation. The identity can be summarized as follows: The wheeling operation is just a graded averaging map in a space enlarging the space of Jacobi diagrams. The purpose of this paper is to present a detailed and self-contained proof of this identity. The proof broadly follows similar calculations in the Alekseev–Meinrenken theory, though the details here are somewhat different, as the algebraic manipulations in the original are replaced with arguments concerning the enumerative combinatorics of formal power series of graphs with graded legs.

Keywords
Lie algebra, Jacobi diagram, wheeling isomorphism, combinatorics
Mathematical Subject Classification 2000
Primary: 17B99, 57M25
Secondary: 05E99
References
Publication
Received: 15 December 2009
Revised: 21 December 2010
Accepted: 4 January 2011
Published: 11 April 2011
Authors
Andrew Kricker
Division of Mathematical Sciences
School of Physical and Mathematical Sciences
Nanyang Technological University
Singapore 637616
Singapore
http://www.ntu.edu.sg/home/ajkricker/