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The Decomposition of Global Conformal Invariants (AM-182)$
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Spyros Alexakis

Print publication date: 2012

Print ISBN-13: 9780691153476

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691153476.001.0001

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A Result on the Structure of Local Riemannian Invariants: The Fundamental Proposition

A Result on the Structure of Local Riemannian Invariants: The Fundamental Proposition

Chapter:
(p.135) Chapter Four A Result on the Structure of Local Riemannian Invariants: The Fundamental Proposition
Source:
The Decomposition of Global Conformal Invariants (AM-182)
Author(s):

Spyros Alexakis

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691153476.003.0004

This chapter sets up a highly complicated proposition (the fundamental proposition 4.13), which is to be proven by an elaborate induction on four parameters. It is organized as follows. Section 4.2 sets up the considerable notational and language conventions needed to state the fundamental Proposition 4.13; it then states the fundamental Proposition and explains how the main algebraic propositions are special cases of it. It also explains the induction using four parameters by which the fundamental proposition will be proven. Section 4.3 distinguishes three cases I, II, III of the hypothesis of Proposition 4.13 and claim three Lemmas, 4.16, 4.19, and 4.24, which correspond to these three cases. Finally, Section 4.4 proves that these three lemmas imply Proposition 4.13. It also asserts certain useful technical lemmas that are also used in the subsequent chapters in this book.

Keywords:   algebraic propositions, lemmas, induction, Riemannian invariants

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