View:

- no detail
- some detail
- full detail

## SURGERY ON MAPS

*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/9780198509240.003.0010
- Subject:
- Mathematics, Geometry / Topology

This chapter gives the definition of a normal map. Killing elements in the relative homotopy group by surgery on a normal map is discussed. The kernel modulesand relative regular homotopy groups of ... More

## Cohomology of Homotopy 2-types

*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/9780198832973.003.0005
- Subject:
- Mathematics, Computational Mathematics / Optimization, Geometry / Topology

This chapter introduces some of the basic ingredients in the classification of homotopy 2-types and describes datatypes and algorithms for implementing them on a computer. These are illustrated using ... More

## Topological Methods for Description of Quantum Many-Body Systems

*Lucjan Jacak, Piotr Sitko, Konrad Wieczorek, and Arkadiusz Wojs*

### in Quantum Hall systems: Braid groups, composite fermions and fractional charge

- Published in print:
- 2003
- Published Online:
- January 2010
- ISBN:
- 9780198528708
- eISBN:
- 9780191713477
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198528708.003.0002
- Subject:
- Physics, Condensed Matter Physics / Materials, Theoretical, Computational, and Statistical Physics

This chapter presents a topological description of quantum many-body systems within the Feynman path integration formalism. Configuration spaces for the system of two particles on the one-dimensional ... More

## Continuous Structures

*VOLOVIK GRIGORY E.*

### in The Universe in a Helium Droplet

- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780199564842
- eISBN:
- 9780191709906
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199564842.003.0016
- Subject:
- Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

When several distinct energy scales are involved, the vacuum symmetry is different for different length scales: the larger the length scale, the more the symmetry is reduced. The interplay of ... More

## Monopoles and Boojums

*VOLOVIK GRIGORY E.*

### in The Universe in a Helium Droplet

- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780199564842
- eISBN:
- 9780191709906
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199564842.003.0017
- Subject:
- Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

This chapter is devoted to point defects such as hedgehogs, Dirac magnetic monopoles, 't Hooft–Polyakov monopole, and nexus. Some of these objects represent composite defects resulting from a ... 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

## Vortices In 3He-B

*VOLOVIK GRIGORY E.*

### in The Universe in a Helium Droplet

- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780199564842
- eISBN:
- 9780191709906
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199564842.003.0014
- Subject:
- Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

This chapter discusses the topology of singular topological defects — defects with singular core of coherence length size — in 3He-B and in quantum chromodynamics, such as conventional mass vortices, ... More

## Topological Classification Of Defects

*VOLOVIK GRIGORY E.*

### in The Universe in a Helium Droplet

- Published in print:
- 2009
- Published Online:
- January 2010
- ISBN:
- 9780199564842
- eISBN:
- 9780191709906
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199564842.003.0013
- Subject:
- Physics, Condensed Matter Physics / Materials, Particle Physics / Astrophysics / Cosmology

The effective metric and effective gauge fields are simulated in superfluids by the inhomogeneity of the superfluid vacuum. In superfluids, many inhomogeneous configurations of the vacuum are stable ... More

View:

- no detail
- some detail
- full detail