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Invariant Prolongation and Detour Complexes

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Symmetries and Overdetermined Systems of Partial Differential Equations

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 144))

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Abstract

In these expository notes we draw together and develop the ideas behind some recent progress in two directions: the treatment of finite type partial differential operators by prolongation, and a class of differential complexes known as detour complexes. This elaborates on a lecture given at the IMA Summer Programme “Symmetries and overdetermined systems of partial differential equations”.

The author would like to thank the Institute for Mathematics & Its Applications, University of Minnesota, and also the organisers of the 2006 Summer Programme there “Symmetries and overdetermined systems of partial differential equations”. Special thanks are due to Tom Branson, a friend, a colleague and a mentor. It is my understanding that his enthusiasm and work contributed significantly to the occurrence and organisation of the meeting. It is part of the tragedy of his departure that he did not get to enjoy the realisation of this event.

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Authors and Affiliations

  1. Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

    A. Rod Gover

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  1. A. Rod Gover
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Editors and Affiliations

  1. School of Mathematical Sciences, The University of Adelaide, SA, 5005, Australia

    Michael Eastwood

  2. School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN, 55455

    Willard Miller Jr.

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Rod Gover, A. (2008). Invariant Prolongation and Detour Complexes. In: Eastwood, M., Miller, W. (eds) Symmetries and Overdetermined Systems of Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 144. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73831-4_19

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