Compactness results for neck-stretching limits of instantons

Abstract

We prove that, under a suitable degeneration of the metric, instantons converge to holomorphic quilts. To prove the main results, we develop estimates for the Yang-Mills heat flow on surfaces and cobordisms.

There is an error in the proof of Proposition 4.9. As such, the following results should be viewed as conjectural until the gap is fixed: Theorem 4.1, Lemma 4.2, and the results of Section 4.2. For more specific details, see the red comments in the proof of Proposition 4.9 in v5

References in corpus (3)

• Quilted Floer Cohomology
• On the components of the gauge group for PU(r)-bundles
• Four-manifold invariants from higher-rank bundles

Cited by in corpus (2)

• Higher-rank instanton cohomology and the quilted Atiyah-Floer conjecture
• An index relation for the quilted Atiyah-Floer conjecture