Instantons and Four-manifolds |
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2-forms 4-manifold action adjoint anti-self-dual argument b₁ ball bounded Chern Chern class cobordism cohomology complex compute concentrated instanton conformally invariant construction convergent coordinates curvature cutoff function cylinder defined denote diffeomorphism differential dimension dimensional Donaldson's Theorem dwb(w elliptic elliptic complex elliptic operators equivariant exists finite fixed follows framed cobordism Fredholm gauge equivalent gauge transformations geometry H₁ H₁(M H²(M Hence Hilbert space homology homotopy implies instanton intersection form invertible LEMMA Lie algebra linear manifold metric g moduli space N¹(ad nonlinear norm operator positive definite principal bundle proof PROPOSITION prove reducible connections Riemannian satisfies self-dual connections singular smooth Sobolev Sobolev spaces solutions structure tangent Taubes topological trivial vanishes vector bundle Weitzenböck formula Yang-Mills equations