Equivariant Gluing Theory on Regular Instanton Moduli Spaces

Abstract

We follow the idea of gluing theory in instanton moduli spaces and discuss the case when there is a finite group Γ acting on the 4-manifolds X₁, X₂ with x₁, x₂ as isolated fixed points, how to glue two Γ-invariant ASD connections over X₁, X₂ together to get a Γ-invariant ASD connection on the connected sum X₁ # X₂.

Keywords

Instanton moduli space / equivariant gluing theory

References

[1] AustinD. SO(3)-instantons on L(p,q) × R. J. Differential Geom., 1990, 32(2): 383-413

[2] BuchdahlNP, KwasikS, SchultzR. One fixed point actions on low-dimensional spheres. Invent. Math., 1990, 102(3): 633-662

[3] DonaldsonSK, KronheimerPBThe Geometry of Four-manifolds, 1990, New York, Oxford University Press

[4] FintushelR, SternR. Pseudofree orbifolds. Ann. of Math. (2), 1985, 122(2): 335-364

[5] FurutaM. A remark on a fixed point of finite group action on S⁴. Topology, 1989, 28(1): 35-38

[6] FurutaM. On self-dual pseudo-connections on some orbifolds. Math. Z., 1992, 209(3): 319-337

[7] LawsonHB, MichelsohnM-LSpin Geometry, 1990, Princeton, NJ, Princeton University Press

[8] UhlenbeckK. Removable singularities in Yang–Mills fields. Comm. Math. Phys., 1982, 83(1): 11-29

RIGHTS & PERMISSIONS

Peking University

Just Accepted

This article has successfully passed peer review and final editorial review, and will soon enter typesetting, proofreading and other publishing processes. The currently displayed version is the accepted final manuscript. The officially published version will be updated with format, DOI and citation information upon launch. We recommend that you pay attention to subsequent journal notifications and preferentially cite the officially published version. Thank you for your support and cooperation.