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## BUNDLES

*Andrew Ranicki*

### in Algebraic and Geometric Surgery

- Published in print:
- 2002
- Published Online:
- September 2007
- ISBN:
- 9780198509240
- eISBN:
- 9780191708725
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198509240.003.0005
- Subject:
- Mathematics, Geometry / Topology

This chapter brings together the basic properties of fibre bundles, fibrations, and vector bundles required in surgery theory. The tangent and normal bundles of a manifold are introduced. The ... More

## Gauge theories and fibre-bundle spaces

*Frank Arntzenius*

### in Space, Time, and Stuff

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199696604
- eISBN:
- 9780191738333
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199696604.003.0006
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science

This chapter discusses the implications of gauge theories for our conception of properties, and for the reality of fibre-bundle spaces. One way of understanding such theories is to claim that the ... More

## What is a gauge theory?

*Richard Healey*

### in Gauging What's Real: The Conceptual Foundations of Gauge Theories

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199287963
- eISBN:
- 9780191713453
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199287963.003.0001
- Subject:
- Philosophy, Philosophy of Science

This chapter explains what is meant by a gauge theory. It states the origins of the term ‘gauge’, and describes the prominent role of gauge theories in contemporary physics. Using the theory of ... More

## Composite Summary of Cerebral White Matter Fiber Pathways in the Rhesus Monkey

*Jeremy D. Schmahmann and Deepak N. Pandya*

### in Fiber Pathways of the Brain

- Published in print:
- 2006
- Published Online:
- May 2009
- ISBN:
- 9780195104233
- eISBN:
- 9780199864294
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195104233.003.0027
- Subject:
- Neuroscience, Techniques, Disorders of the Nervous System

This chapter presents a series of diagrams of rostral to caudal coronal sections of the brain of a rhesus monkey that illustrate in a composite manner the association, commissural, projection, and ... More

## Calculus as geometry

*Frank Arntzenius*

### in Space, Time, and Stuff

- Published in print:
- 2012
- Published Online:
- May 2012
- ISBN:
- 9780199696604
- eISBN:
- 9780191738333
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199696604.003.0008
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science

This chapter argues that calculus, the theory of differentiation and integration that permeates modern science, can be formulated as a purely geometric theory, which does not entail the existence of ... More

## Classical gauge theories

*Richard Healey*

### in Gauging What's Real: The Conceptual Foundations of Gauge Theories

- Published in print:
- 2007
- Published Online:
- January 2008
- ISBN:
- 9780199287963
- eISBN:
- 9780191713453
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199287963.003.0003
- Subject:
- Philosophy, Philosophy of Science

This chapter extends the analysis of classical gauge theories to encompass both non-Abelian Yang-Mills theories and the general theory of relativity. It explains what is meant by a non-Abelian ... More

## Differential geometry, topology and fibre bundles

*Reinhold A. Bertlmann*

### in Anomalies in Quantum Field Theory

- Published in print:
- 2000
- Published Online:
- February 2010
- ISBN:
- 9780198507628
- eISBN:
- 9780191706400
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198507628.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces all necessary mathematical concepts. Section 2.1 briefly summarizes some topological definitions. Section 2.2 explains the homotopy of maps and the homotopy of groups. Section ... More

## Superior Longitudinal Fasciculus and Arcuate Fasciculus

*Jeremy D. Schmahmann and Deepak N. Pandya*

### in Fiber Pathways of the Brain

- Published in print:
- 2006
- Published Online:
- May 2009
- ISBN:
- 9780195104233
- eISBN:
- 9780199864294
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195104233.003.0013
- Subject:
- Neuroscience, Techniques, Disorders of the Nervous System

The superior longitudinal fasciculus (SLF) and the arcuate fasciculus (AF) have long been considered synonymous in the human, and these names have been used interchangeably. According to observations ... More

## Weyl's “Purely Infinitesimal” Constitution of Field Physics

*Thomas Ryckman*

### in The Reign of Relativity: Philosophy in Physics 1915-1925

- Published in print:
- 2005
- Published Online:
- April 2005
- ISBN:
- 9780195177176
- eISBN:
- 9780199835324
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0195177177.003.0006
- Subject:
- Philosophy, Philosophy of Science

It is shown how Weyl intertwined phenomenological analysis and mathematical construction in building the foundation of his “pure infinitesimal geometry” underlying gravitation and electromagnetism. ... More

## Muscle mechanics I: intact single muscle fibres

*Haruo Sugi and Teizo Tsuchiya*

### in Current Methods in Muscle Physiology: Advantages, Problems and Limitations

- Published in print:
- 1998
- Published Online:
- March 2012
- ISBN:
- 9780198523970
- eISBN:
- 9780191724480
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198523970.003.0001
- Subject:
- Neuroscience, Techniques

In the field of muscle mechanics, muscle physiologists attempt to obtain information about molecular events responsible for muscle contraction, i.e. the myofilament sliding, mainly by applying ... More

## Electrophysiological approaches to the study of axons

*PETER K. STYS and JEFFERY D. KOCSIS*

### in The Axon: Structure, Function and Pathophysiology

- Published in print:
- 1995
- Published Online:
- May 2009
- ISBN:
- 9780195082937
- eISBN:
- 9780199865802
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195082937.003.0017
- Subject:
- Neuroscience, Disorders of the Nervous System

This chapter discusses the theory and practice of some of the more common techniques devised for recording electrical activity in single axons or fiber bundles. It focuses on electrophysiological ... More

## Product Spaces and Fiber Bundles

*Tim Maudlin*

### in New Foundations for Physical Geometry: The Theory of Linear Structures

- Published in print:
- 2014
- Published Online:
- April 2014
- ISBN:
- 9780198701309
- eISBN:
- 9780191771613
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198701309.003.0009
- Subject:
- Philosophy, Logic/Philosophy of Mathematics

Standard topology provides a method of defining a topology on the Cartesian product of two topological spaces. Defining a linear structure on the Cartesian product of two spaces is more involved. The ... More

## Principal Bundles

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0003
- Subject:
- Mathematics, Educational Mathematics

This chapter examines principal bundles. Throughout the chapter, G will be a topological group. It then defines a principal G-bundle and provides a criterion for a map to be a principal G-bundle. ... More

## Homotopy Quotients and Equivariant Cohomology

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0004
- Subject:
- Mathematics, Educational Mathematics

This chapter investigates two candidates for equivariant cohomology and explains why it settles on the Borel construction, also called Cartan's mixing construction. Let G be a topological group and M ... More

## Topology, Manifolds, Dynamical Systems, Measure, and Bundles

*Xin Wei Sha*

### in Poiesis and Enchantment in Topological Matter

- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780262019514
- eISBN:
- 9780262318914
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262019514.003.0006
- Subject:
- Philosophy, Aesthetics

This is the core chapter, introducing concepts that articulate continua, continuous substance, and continuous process. These concepts find precise and deep forms in point set topology, topological ... More

## Spectral Sequences

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0006
- Subject:
- Mathematics, Educational Mathematics

This chapter focuses on spectral sequences. The spectral sequence is a powerful computational tool in the theory of fiber bundles. First introduced by Jean Leray in the 1940s, it was further refined ... More

##
Equivariant Cohomology of *S*^{2} Under Rotation

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0007
- Subject:
- Mathematics, Educational Mathematics

This chapter shows how to use the spectral sequence of a fiber bundle to compute equivariant cohomology. As an example, it computes the equivariant cohomology of S2 under the action of S1 by ... More

## Homotopy Groups and CW Complexes

*Loring W. Tu*

### in Introductory Lectures on Equivariant Cohomology: (AMS-204)

- Published in print:
- 2020
- Published Online:
- January 2021
- ISBN:
- 9780691191751
- eISBN:
- 9780691197487
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691191751.003.0002
- Subject:
- Mathematics, Educational Mathematics

This chapter discusses some results about homotopy groups and CW complexes. Throughout this book, one needs to assume a certain amount of algebraic topology. A CW complex is a topological space built ... More

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