## Chern-Simons Theory, Matrix Models, and Topological Strings

*Marcos Mariño*

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568490
- eISBN:
- 9780191717604
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568490.001.0001
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

In recent years, the old idea that gauge theories and string theories are equivalent has been implemented and developed in various ways, and there are by now various models where the string ... More

## APPLICATIONS OF THE TOPOLOGICAL STRING/GAUGE THEORY CORRESPONDENCE

*Marcos Mariño*

### in Chern-Simons Theory, Matrix Models, and Topological Strings

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568490
- eISBN:
- 9780191717604
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568490.003.0010
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter considers two applications of the topological string/gauge theory correspondence. The first application is to Chern-Simons knot and link invariants, and the second application is to ... More

## CHERN–SIMONS THEORY AND KNOT INVARIANTS

*Marcos Mariño*

### in Chern-Simons Theory, Matrix Models, and Topological Strings

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568490
- eISBN:
- 9780191717604
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568490.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

This chapter presents various aspects of Chern-Simons theory. In a groundbreaking paper, Witten (1989) showed that Chern-Simons gauge theory, which is a quantum field theory in three dimensions, ... More

## REPRINT STATISTICAL MECHANICS WITH TOPOLOGICAL CONSTRAINTS: II

*S. F. Edwards*

### in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528531
- eISBN:
- 9780191713415
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528531.003.0011
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter presents a paper showing that the full specification of an assembly of long flexible molecules, needed for a statistical-mechanical study, requires an infinite set of topological ... More

## NOTES ON ‘STATISTICAL MECHANICS WITH TOPOLOGICAL CONSTRAINTS: I & II’

*Edward Witten*

### in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528531
- eISBN:
- 9780191713415
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528531.003.0012
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter discusses Edwards' early work trying to devise a convenient description of topological constraint in order to study the statistical physics of cross-linked polymers, which is related to ... More

## A SCIENTIST FOR ALL SEASONS

*Sir Geoffrey Allen and F.R.S. F.R. Eng.*

### in Stealing the Gold: A celebration of the pioneering physics of Sam Edwards

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198528531
- eISBN:
- 9780191713415
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528531.003.0029
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter describes the history of Sam Edwards within polymer physics from the early days of his exposure, through his insights in seeing what is important, bringing key new insights, inspiring ... More

## The Gordian Knot

*David A. Shore and Eric D. Kupferberg*

### in High Stakes: The Critical Role of Stakeholders in Health Care

- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780195326253
- eISBN:
- 9780199897285
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780195326253.003.0012
- Subject:
- Public Health and Epidemiology, Public Health

This chapter looks at the value in health care in the United States. Section 2.1 considers what we get for the dollars spent in the United States. Section 2.2 identifies the price inflators that are ... More

## Lectures on Geometry

*Edward Witten, Martin Bridson, Helmut Hofer, Marc Lackenby, and Rahul Pandharipande*

*N M J Woodhouse (ed.)*

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198784913
- eISBN:
- 9780191827150
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198784913.001.0001
- Subject:
- Mathematics, Geometry / Topology

This volume contains a collection of papers based on lectures delivered by distinguished mathematicians at Clay Mathematics Institute events over the past few years. Although not explicitly linked, ... More

## 4-Manifolds

*Selman Akbulut*

- Published in print:
- 2016
- Published Online:
- November 2016
- ISBN:
- 9780198784869
- eISBN:
- 9780191827136
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198784869.001.0001
- Subject:
- Mathematics, Geometry / Topology

This book present the topology of smooth 4-manifolds in an intuitive self-contained way. The handlebody theory, and the seiberg-witten theory of 4-manifolds are presented. Also stein and symplectic ... More

## The knowledge–power knot in professionalism: transforming the ‘currency of competition’

*Ellen Kuhlmann*

### in Modernising health care: Reinventing professions, the state and the public

- Published in print:
- 2006
- Published Online:
- March 2012
- ISBN:
- 9781861348586
- eISBN:
- 9781447302810
- Item type:
- chapter

- Publisher:
- Policy Press
- DOI:
- 10.1332/policypress/9781861348586.003.0010
- Subject:
- Public Health and Epidemiology, Public Health

This chapter examines the knowledge-power knot of professionalism. The power of biomedical knowledge is not simply changed through standardisation and EBM. Moreover, ambivalence is embedded in ... More

## Other Minds

*Sergio Balari and Guillermo Lorenzo*

### in Computational Phenotypes: Towards an Evolutionary Developmental Biolinguistics

- Published in print:
- 2012
- Published Online:
- January 2013
- ISBN:
- 9780199665464
- eISBN:
- 9780191746116
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199665464.003.0007
- Subject:
- Linguistics, Psycholinguistics / Neurolinguistics / Cognitive Linguistics, Historical Linguistics

This chapter defends the proposition that minds other than human are probably endowed with a system of computation homologous to that of FL in terms of computational complexity. It defends the idea ... More

## At the Crossroads: The Intercession of Diaghilev

*Charles M. Joseph*

### in Stravinsky and Balanchine: A Journey of Invention

- Published in print:
- 2002
- Published Online:
- October 2013
- ISBN:
- 9780300087123
- eISBN:
- 9780300129342
- Item type:
- chapter

- Publisher:
- Yale University Press
- DOI:
- 10.12987/yale/9780300087123.003.0002
- Subject:
- Society and Culture, Cultural Studies

This chapter talks about Serge Pavlovich Diaghilev—a figure who stands at the intersection of the Stravinsky-Balanchine union. In retracing the origins of the composer and choreographer's ... More

## Braids

*Aaron Abrams*

### in Office Hours with a Geometric Group Theorist

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691158662
- eISBN:
- 9781400885398
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691158662.003.0018
- Subject:
- Mathematics, Geometry / Topology

This chapter deals with mathematical braids, an idealized abstraction of the familiar hair and bread braids. In a mathematical braid, the “strings” remain separate at the ends rather than being fused ... More

## Two Lectures on the Jones Polynomial and Khovanov Homology

*Edward Witten*

### in Lectures on Geometry

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198784913
- eISBN:
- 9780191827150
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198784913.003.0001
- Subject:
- Mathematics, Geometry / Topology

In the first of these two lectures I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret ... More

## Elementary Knot Theory

*Marc Lackenby*

### in Lectures on Geometry

- Published in print:
- 2017
- Published Online:
- May 2017
- ISBN:
- 9780198784913
- eISBN:
- 9780191827150
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198784913.003.0002
- Subject:
- Mathematics, Geometry / Topology

This is an elementary survey of knot theory. It is a well developed, but there remain several notoriously intractable problems about knots and links, many of which are surprisingly easy to state. The ... More

## Path Components and the Fundamental Group

*Graham Ellis*

### in An Invitation to Computational Homotopy

- Published in print:
- 2019
- Published Online:
- November 2019
- ISBN:
- 9780198832973
- eISBN:
- 9780191871375
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198832973.003.0001
- Subject:
- Mathematics, Computational Mathematics / Optimization, Geometry / Topology

This chapter introduces some of the basic concepts of algebraic topology and describes datatypes and algorithms for implementing them on a computer. The basic concepts include: regular CW-complex, ... More

## Needles in a Haystack: the Class NP

*Cristopher Moore and Stephan Mertens*

### in The Nature of Computation

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199233212
- eISBN:
- 9780191775079
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199233212.003.0004
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

NP refers to a class of decision problems in which yes-instances are easy to verify. That is: a decision problem is in NP if, whenever the answer for a particular instance is ‘yes’, there is a simple ... More

## For Tying Knots: Who invented language and mathematics?

*Vinciane Despret*

### in What Would Animals Say If We Asked the Right Questions?

- Published in print:
- 2016
- Published Online:
- January 2017
- ISBN:
- 9780816692378
- eISBN:
- 9781452954394
- Item type:
- chapter

- Publisher:
- University of Minnesota Press
- DOI:
- 10.5749/minnesota/9780816692378.003.0020
- Subject:
- Philosophy, General

This chapter explores animals’ capacity for mathematics, arithmetic, and recognizing numerical difference, whether through cognitive ability or gestalt sensing. In an analysis of a knot-tying ape, ... More

## Lattice Models of Linear and Ring Polymers

*E.J. Janse Van Rensburg*

### in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.003.0001
- Subject:
- Mathematics, Mathematical Physics

In Chapter 1 the self-avoiding walk connective constant, growth constant and subadditivity are introduced. Concatenation and the supermultiplicativity of lattice polygons are discussed. Scaling, ... More

## Self-avoiding walks and polygons

*E.J. Janse Van Rensburg*

### in The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles

- Published in print:
- 2015
- Published Online:
- August 2015
- ISBN:
- 9780199666577
- eISBN:
- 9780191748653
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666577.003.0007
- Subject:
- Mathematics, Mathematical Physics

Chapter 7 provides an overview of self-avoiding walks, polygons and half-space walks. The Hammersley-Welsh construction is discussed, as well as the bridge decomposition of half-space walks. Loops, ... More