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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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