The Atiyah-jones Conjecture
نویسندگان
چکیده
The purpose of this note is to announce our proof of the AtiyahJones conjecture concerning the topology of the moduli spaces of based su(2)instantons over s4 . Full details and proofs appear in our paper [BHMM1].
منابع مشابه
Atiyah – Jones conjecture for blown - up surfaces
We show that if the Atiyah–Jones conjecture holds for a surface X, then it also holds for the blow-up of X at a point. Since the conjecture is known to hold for P2 and for ruled surfaces, it follows that the conjecture is true for all rational surfaces. Given a 4-manifold X, let MIk(X) denote the moduli space of rank 2 instantons on X with charge k and let Ck(X) denote the space of all connecti...
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We show that if the Atiyah–Jones conjecture holds for a surface X, then it also holds for the blow-up of X at a point. Since the conjecture is known to hold for P2 and for ruled surfaces, it follows that the conjecture is true for all rational surfaces. Given a 4-manifold X, let MIk(X) denote the moduli space of rank 2 instantons on X with charge k and let Ck(X) denote the space of all gauge eq...
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is minimal precisely when the curvature FA is anti-self dual, i.e. FA = −∗FA, in which case A is called an instanton of charge k on X. Let MIk(X) denote the moduli space of framed instantons on X with charge k and let Ck(X) denote the space of all framed gauge equivalence classes of connections on X with charge k. In 1978, Atiyah and Jones [AJ] conjectured that the inclusion MIk(X) → Ck(X) indu...
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Given a 4-manifold X, let MIk(X) denote the moduli space of rank 2 instantons on X with charge k and let Ck(X) denote the space of all gauge equivalence classes of connections on X with charge k. In 1978, Atiyah and Jones [AJ] conjectured that the inclusion MIk(X) → Ck(X) induces an isomorphism in homology and homotopy through a range that grows with k. The original statement of the conjecture ...
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