The minimal Hirsch–Brown model via classical Hodge theory

Christopher Allday and Volker Puppe

Vol. 226 (2006), No. 1, 41–51

DOI: 10.2140/pjm.2006.226.41

Abstract

In our book on cohomological methods in transformation groups the minimal Hirsch–Brown model was used to good effect. The construction of the model there, however, was rather abstract. Here, for smooth compact connected Lie group actions on smooth closed manifolds, we give a much more explicit construction of the minimal Hirsch–Brown model using operators from classical Hodge theory and the Cartan model.

Keywords

Cartan model, Hirsch–Brown model, Hodge theory, canonical extension

Mathematical Subject Classification 2000

Primary: 57S15, 57R91

Secondary: 57R17, 53D05

Milestones

Received: 15 October 2004

Revised: 29 April 2005

Accepted: 21 May 2005

Published: 1 July 2006