PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees

Paul M.N. Feehan, Thomas G. Leness

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

In this article, a continuation of [10], we complete the proof - for a broad class of four - manifolds - of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c - 2, where c = -1/4(7χ + 11σ) and χ and σ are the Euler characteristic and signature of the four-manifold. We use our computations of Chern classes for the virtual normal bundles for the Seiberg-Witten strata from the companion article [10], a comparison of all the orientations, and the PU(2) monopole cobordism to compute pairings with the links of level-zero Seiberg-Witten moduli subspaces of the moduli space of PU(2) monopoles. These calculations then allow us to compute low-degree Donaldson invariants in terms of Seiberg-Witten invariants and provide a partial verification of Witten's conjecture.

Original languageEnglish (US)
Pages (from-to)135-212
Number of pages78
JournalJournal fur die Reine und Angewandte Mathematik
Volume538
DOIs
StatePublished - 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees'. Together they form a unique fingerprint.

Cite this