The L 2 metric in gauge theory: an introduction and some applications

David Groisser

Banach Center Publications (1997)

  • Volume: 39, Issue: 1, page 317-329
  • ISSN: 0137-6934

Abstract

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We discuss the geometry of the Yang-Mills configuration spaces and moduli spaces with respect to the L 2 metric. We also consider an application to a de Rham-theoretic version of Donaldson’s μ-map.

How to cite

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Groisser, David. "The $L^2$ metric in gauge theory: an introduction and some applications." Banach Center Publications 39.1 (1997): 317-329. <http://eudml.org/doc/208670>.

@article{Groisser1997,
abstract = {We discuss the geometry of the Yang-Mills configuration spaces and moduli spaces with respect to the $L^2$ metric. We also consider an application to a de Rham-theoretic version of Donaldson’s μ-map.},
author = {Groisser, David},
journal = {Banach Center Publications},
keywords = {moduli space of Yang-Mills connections; metric; Pontryagin index; intersection form; collar region},
language = {eng},
number = {1},
pages = {317-329},
title = {The $L^2$ metric in gauge theory: an introduction and some applications},
url = {http://eudml.org/doc/208670},
volume = {39},
year = {1997},
}

TY - JOUR
AU - Groisser, David
TI - The $L^2$ metric in gauge theory: an introduction and some applications
JO - Banach Center Publications
PY - 1997
VL - 39
IS - 1
SP - 317
EP - 329
AB - We discuss the geometry of the Yang-Mills configuration spaces and moduli spaces with respect to the $L^2$ metric. We also consider an application to a de Rham-theoretic version of Donaldson’s μ-map.
LA - eng
KW - moduli space of Yang-Mills connections; metric; Pontryagin index; intersection form; collar region
UR - http://eudml.org/doc/208670
ER -

References

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  3. [D1] S. K. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983), 279-315. Zbl0507.57010
  4. [D2] S. K. Donaldson, Compactification and completion of Yang-Mills moduli spaces, in: Differential Geometry, Proc. Conf. Peniscola 1988, F. J. Carreras et al. (ed.), Lecture Notes in Math. 1410, Springer, Berlin, 1989, 145-160. 
  5. [DK] S. K. Donaldson, P. Kronheimer, The Geometry of Four-Manifolds, Oxford University Press, New York, 1990. Zbl0820.57002
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  9. [G2] D. Groisser, Curvature of Yang-Mills moduli spaces near the boundary, I, Comm. Anal. Geom. 1 (1993), 139-216. Zbl0846.58012
  10. [G3] D. Groisser, Totally geodesic boundaries of Yang-Mills moduli spaces, Preprint, 1996. 
  11. [GP1] D. Groisser and T. H. Parker, The Riemannian geometry of the Yang-Mills Moduli Space, Comm. Math. Phys. 112 (1987), 663-689. Zbl0637.53037
  12. [GP2] D. Groisser and T. H. Parker, The geometry of the Yang-Mills moduli space for definite manifolds, J. Differential Geom. 29 (1989), 499-544. Zbl0679.53024
  13. [GP3] D. Groisser and T. H. Parker, Semiclassical Yang-Mills Theory I, Instantons, Comm. Math. Phys. 135 (1990), 101-140. Zbl0792.53024
  14. [GP4] D. Groisser and T. H. Parker, Differential forms on the Yang-Mills moduli space, in preparation. 
  15. [GS] D. Groisser and L. Sadun, Simple type and the boundary of moduli space, in preparation. Zbl0973.57014
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  17. [K] K. Kobayashi, Three Riemannian metrics on the moduli space of 1-instantons over 𝐂𝐏 2 , Hiroshima Math. J. 19 (1989), 243-249. Zbl0715.53028
  18. [MM] K. B. Marathe and G. Martucci, The Mathematical Foundations of Gauge Theories, North-Holland, Amsterdam, 1992. Zbl0920.58079
  19. [M] T. Matumoto, Three Riemannian metrics on the moduli space of BPST-instantons over S 4 , Hiroshima Math. J. 19 (1989), 221-224. Zbl0736.58006
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  21. [S] I. M. Singer, The Geometry of the Orbit Space for Nonabelian Gauge Theories, Phys. Scripta 24 (1981), 817-820. Zbl1063.81623

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