Finite group actions on the moduli space of self-dual connections. I
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- by Yong Seung Cho PDF
- Trans. Amer. Math. Soc. 323 (1991), 233-261 Request permission
Abstract:
Let $M$ be a smooth simply connected closed $4$-manifold with positive definite intersection form. Suppose a finite group $G$ acts smoothly on $M$. Let $\pi :E \to M$ be the instanton number one quaternion line bundle over $M$ with a smooth $G$-action such that $\pi$ is an equivariant map. We first show that there exists a Baire set in the $G$-invariant metrics on $M$ such that the moduli space $\mathcal {M}_ * ^G$ of $G$-invariant irreducible self-dual connections is a manifold. By utilizing the $G$-transversality theory of $\text {T}$. Petrie, we then identify cohomology obstructions to globally perturbing the full space ${\mathcal {M}_ * }$ of irreducible self-dual connections to a $G$-manifold when $G = {{\mathbf {Z}}_2}$ and the fixed point set of the ${\mathbf {Z}}_2$ action on $M$ is a nonempty collection of isolated points and Riemann surfaces.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 323 (1991), 233-261
- MSC: Primary 58D15; Secondary 53C05, 57S17, 58B20, 58G10
- DOI: https://doi.org/10.1090/S0002-9947-1991-1010409-2
- MathSciNet review: 1010409