Methods and Applications of Analysis

Volume 24 (2017)

Number 2

Special issue dedicated to Henry B. Laufer on the occasion of his 70th birthday: Part 2

Guest Editors: Stephen S.-T. Yau (Tsinghua University, China); Gert-Martin Greuel (University of Kaiserslautern, Germany); Jonathan Wahl (University of North Carolina, USA); Rong Du (East China Normal University, China); Yun Gao (Shanghai Jiao Tong University, China); and Huaiqing Zuo (Tsinghua University, China)

The Grauert–Grothendieck complex on differentiable spaces and a sheaf complex of Brylinski

Pages: 321 – 332



Markus J. Pflaum (Department of Mathematics, University of Colorado, Boulder, Co., U.S.A.)

Hessel Posthuma (Korteweg-de Vries Institute for Mathematics, University of Amsterdam, The Netherlands)

Xiang Tang (Department of Mathematics, Washington University, St. Louis, Missouri, U.S.A.)


We use the Grauert–Grothendieck complex on differentiable spaces to study basic relative forms on the inertia space of a compact Lie group action on a manifold. We prove that the sheaf complex of basic relative forms on the inertia space is a fine resolution of Bryliski’s sheaf of functions on the inertia space.


Grauert–Grothendieck complex, relative basic form, differentiable space

2010 Mathematics Subject Classification

32C18, 32S20

Full Text (PDF format)

Received 20 May 2016

Accepted 29 November 2016

Published 3 January 2018