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Abundant Earth: Toward an Ecological Civilization

Eileen Crist

Published in print:
2019
Published Online:
September 2019
ISBN:
9780226596778
eISBN:
9780226596945
Item type:
book
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226596945.001.0001
Subject:
Environmental Science, Environmental Studies

Abundant Earth documents the loss of biodiversity underway and lays out the drivers of this destruction. It goes beyond the litany of causes—a growing population, rising livestock numbers, expanding ... More


Maps and vector bundles

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0005
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

This discussion of maps and vector bundles covers the pull-back construction; pull-backs and Grassmannians; pull-back of differential forms and push-forward of vector fields; invariant forms and ... More


Trace of the Generating Series

Xinyi Yuan, Shou-Wu Zhang, and Wei Zhang

in The Gross-Zagier Formula on Shimura Curves

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691155913
eISBN:
9781400845644
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691155913.003.0004
Subject:
Mathematics, Number Theory

This chapter proves the theorem that asserts the modularity of the generating series and the theorem dealing with abelian varieties parametrized by Shimura curves. Before presenting the proofs, the ... More


Principal bundles

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0010
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

This chapter examines principal bundles, which is defined as the Lie group analog of a vector bundle. It covers principal bundles constructed from vector bundles; examples of Lie group quotients; ... More


Covariant derivatives and connections

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0011
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

This chapter examines the related notions of covariant derivative and connection. It covers the space of covariant derivatives. It also gives a relatively straightforward construction of a covariant ... More


Restoring Abundant Earth

Eileen Crist

in Abundant Earth: Toward an Ecological Civilization

Published in print:
2019
Published Online:
September 2019
ISBN:
9780226596778
eISBN:
9780226596945
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226596945.003.0010
Subject:
Environmental Science, Environmental Studies

“Restoring Abundant Earth” elaborates on pulling back, involving large-scale protection of land and seas—the best way to save biodiversity. Drawing on Earth system science and ecological writings, ... More


Vector bundles with ℂn as fiber

Clifford Henry Taubes

in Differential Geometry: Bundles, Connections, Metrics and Curvature

Published in print:
2011
Published Online:
December 2013
ISBN:
9780199605880
eISBN:
9780191774911
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199605880.003.0006
Subject:
Mathematics, Geometry / Topology, Mathematical Physics

Just as there are vector spaces over ℂ, there are vector bundles whose fibres can be consistently viewed as ℂn for some n. This chapter first defines these objects and then provides number of ... More


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