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1997 | 39 | 1 | 317-329
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
39
Numer
1
Strony
317-329
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Department of Mathematics, University of Florida Gainesville, Florida 32611, USA
Bibliografia
  • [CE] J. Cheeger and D. G. Ebin, Comparison Theorems in Riemannian Geometry, North-Holland, Amsterdam, 1975.
  • [DMM] H. Doi, Y. Matsumoto, and T. Matumoto, An explicit formula of the metric on the moduli space of BPST-instantons over $S^4$, in: A Fête of Topology, Academic Press, 1987, 543-556.
  • [D1] S. K. Donaldson, An application of gauge theory to four-dimensional topology, J. Differential Geom. 18 (1983), 279-315.
  • [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.
  • [DK] S. K. Donaldson, P. Kronheimer, The Geometry of Four-Manifolds, Oxford University Press, New York, 1990.
  • [F] P. Feehan, Geometry of the ends of the moduli space of anti-self-dual connections, J. Differential Geom. 42 (1995), 465-553.
  • [FU] D. S. Freed and K. K. Uhlenbeck, Instantons and Four-Manifolds, second edition, Springer, New York, 1991.
  • [G1] D. Groisser, The geometry of the moduli space of ${\bf CP^2}$ instantons, Invent. Math. 99 (1990), 393-409.
  • [G2] D. Groisser, Curvature of Yang-Mills moduli spaces near the boundary, I, Comm. Anal. Geom. 1 (1993), 139-216.
  • [G3] D. Groisser, Totally geodesic boundaries of Yang-Mills moduli spaces, Preprint, 1996.
  • [GP1] D. Groisser and T. H. Parker, The Riemannian geometry of the Yang-Mills Moduli Space, Comm. Math. Phys. 112 (1987), 663-689.
  • [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.
  • [GP3] D. Groisser and T. H. Parker, Semiclassical Yang-Mills Theory I, Instantons, Comm. Math. Phys. 135 (1990), 101-140.
  • [GP4] D. Groisser and T. H. Parker, Differential forms on the Yang-Mills moduli space, in preparation.
  • [GS] D. Groisser and L. Sadun, Simple type and the boundary of moduli space, in preparation.
  • [H] L. Habermann, On the geometry of the space of Sp(1)-instantons with Pontrjagin index 1 on the 4-sphere, Ann. Global Anal. Geom. 6 (1988), 3-29.
  • [K] K. Kobayashi, Three Riemannian metrics on the moduli space of 1-instantons over ${\bf CP^2}$, Hiroshima Math. J. 19 (1989), 243-249.
  • [MM] K. B. Marathe and G. Martucci, The Mathematical Foundations of Gauge Theories, North-Holland, Amsterdam, 1992.
  • [M] T. Matumoto, Three Riemannian metrics on the moduli space of BPST-instantons over $S^4$, Hiroshima Math. J. 19 (1989), 221-224.
  • [MV] P. K. Mitter and C. M. Viallet, On the bundle of connections and the gauge orbit manifold in Yang-Mills theory, Comm. Math. Phys. 79 (1981), 457-472.
  • [S] I. M. Singer, The Geometry of the Orbit Space for Nonabelian Gauge Theories, Phys. Scripta 24 (1981), 817-820.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv39z1p317bwm
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