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The Decomposition of Global Conformal Invariants (AM-182)

Spyros Alexakis

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.001.0001
Subject:
Mathematics, Geometry / Topology

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question ... More


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

Spyros Alexakis

in The Decomposition of Global Conformal Invariants (AM-182)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.003.0004
Subject:
Mathematics, Geometry / Topology

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 ... More


The Inductive Step of the Fundamental Proposition: The Simpler Cases

Spyros Alexakis

in The Decomposition of Global Conformal Invariants (AM-182)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.003.0005
Subject:
Mathematics, Geometry / Topology

This chapter takes up the proof of Lemmas 4.16 and 4.19, which are easier than Lemma 4.24. The proof of these two lemmas relies on the study of the first conformal variation of the assumption of ... More


The Inductive Step of the Fundamental Proposition: The Hard Cases, Part I

Spyros Alexakis

in The Decomposition of Global Conformal Invariants (AM-182)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.003.0006
Subject:
Mathematics, Geometry / Topology

This chapter takes up the proof of Lemma 4.24, which has two cases, A and B. The strategy goes as follows: It first repeats the ideas from Chapter 5 and derives a new local equation from the ... More


The Inductive Step of the Fundamental Proposition: The Hard Cases, Part II

Spyros Alexakis

in The Decomposition of Global Conformal Invariants (AM-182)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.003.0007
Subject:
Mathematics, Geometry / Topology

This chapter takes up the proof of Lemma 4.24 in Case B; this completes the inductive step of the proof of the fundamental proposition 4.13. The chapter recalls that Lemma 4.24 applies when all ... More


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