The configuration space of gauge theory on open manifolds of bounded geometry

Jürgen Eichhorn; Gerd Heber

Banach Center Publications (1997)

  • Volume: 39, Issue: 1, page 269-286
  • ISSN: 0137-6934

Abstract

top
We define suitable Sobolev topologies on the space 𝒞 P ( B k , f ) of connections of bounded geometry and finite Yang-Mills action and the gauge group and show that the corresponding configuration space is a stratified space. The underlying open manifold is assumed to have bounded geometry.

How to cite

top

Eichhorn, Jürgen, and Heber, Gerd. "The configuration space of gauge theory on open manifolds of bounded geometry." Banach Center Publications 39.1 (1997): 269-286. <http://eudml.org/doc/208667>.

@article{Eichhorn1997,
abstract = {We define suitable Sobolev topologies on the space $\{\mathcal \{C\}\}_P(B_k,f)$ of connections of bounded geometry and finite Yang-Mills action and the gauge group and show that the corresponding configuration space is a stratified space. The underlying open manifold is assumed to have bounded geometry.},
author = {Eichhorn, Jürgen, Heber, Gerd},
journal = {Banach Center Publications},
keywords = {space of connections; finite Yang-Mills action; gauge group; configuration space; stratified space},
language = {eng},
number = {1},
pages = {269-286},
title = {The configuration space of gauge theory on open manifolds of bounded geometry},
url = {http://eudml.org/doc/208667},
volume = {39},
year = {1997},
}

TY - JOUR
AU - Eichhorn, Jürgen
AU - Heber, Gerd
TI - The configuration space of gauge theory on open manifolds of bounded geometry
JO - Banach Center Publications
PY - 1997
VL - 39
IS - 1
SP - 269
EP - 286
AB - We define suitable Sobolev topologies on the space ${\mathcal {C}}_P(B_k,f)$ of connections of bounded geometry and finite Yang-Mills action and the gauge group and show that the corresponding configuration space is a stratified space. The underlying open manifold is assumed to have bounded geometry.
LA - eng
KW - space of connections; finite Yang-Mills action; gauge group; configuration space; stratified space
UR - http://eudml.org/doc/208667
ER -

References

top
  1. [1] N. Bourbaki, Éléments de mathématique, Fasc. XXXIII, Variétés différentielles et analytiques, Fascicule de résultates (Paragraphes 1 à 7), Hermann, Paris, 1971. Zbl0206.50402
  2. [2] N. Bourbaki, Éléments de mathématique, Fasc. XXXVIII, Groupes et algèbres de Lie, Hermann, Paris, 1972. Zbl0244.22007
  3. [3] J. Eichhorn, Elliptic differential operators on noncompact manifolds, in: Seminar Analysis of the Karl-Weierstrass-Institute of Mathematics (Berlin, 1986/87), Teubner-Texte Math. 106, Leipzig, 1988, 4-169. 
  4. [4] J. Eichhorn, Gauge theory on open manifolds of bounded geometry, Internat. J. Modern Phys. A 7 (1992), 3927-3977. 
  5. [5] J. Eichhorn, The manifold structure of maps between open manifolds, Ann. Global Anal. Geom. 11 (1993), 253-300. Zbl0840.58014
  6. [6] J. Eichhorn, Spaces of Riemannian metrics on open manifolds, Results Math. 27 (1995), 256-283. Zbl0833.58008
  7. [7] J. Eichhorn, The boundedness of connection coefficients and their derivatives, Math. Nachr. 152 (1991), 145-158. Zbl0736.53031
  8. [8] J. Eichhorn, Differential operators with Sobolev coefficients, in preparation. 
  9. [9] J. Eichhorn, The invariance of Sobolev spaces over noncompact manifolds, in: Symposium 'Partial Differential Equations' (Holzhau, 1988), Teubner-Texte Math. 112, Leipzig, 1989, 73-107. 
  10. [10] J. Eichhorn and J. Fricke, The module structure theorem for Sobolev spaces on open manifolds, Math. Nachr. (to appear). Zbl0954.46020
  11. [11] J. Eichhorn and R. Schmid, Form preserving diffeomorphisms on open manifolds, Math. Nachr. (to appear). Zbl0862.58007
  12. [12] A. E. Fischer, The internal symmetry group of a connection on a principal fibre bundle with applications to gauge field theory, Comm. Math. Phys. 113 (1987), 231-262. Zbl0638.53039
  13. [13] G. Heber, Die Topologie des Konfigurationsraumes der Yang-Mills Theorie über offenen Mannigfaltigkeiten beschränkter Geometrie, Ph.D. thesis, Greifswald, 1994. 
  14. [14] W. Kondracki and J. Rogulski, On the stratification of the orbit space for the action of automorphisms on connections, Dissertationes Math. (Rozprawy Mat.) 250 (1986). Zbl0614.57025
  15. [15] W. Kondracki and P. Sadowski, Geometric structure on the orbit space of gauge connections, J. Geom. Phys. 3 (1986), 421-434. Zbl0624.53055

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.