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On Casson-type instanton moduli spaces over negative definite 4-manifolds

Lobb, Andrew; Zentner, Raphael

On Casson-type instanton moduli spaces over negative definite 4-manifolds Thumbnail


Authors

Raphael Zentner



Abstract

Recently Andrei Teleman considered instanton moduli spaces over negative definite 4-manifolds X with b2(X) ≥ 1. If b2(X) is divisible by four and b1(X) = 1 a gauge-theoretic invariant can be defined; it is a count of flat connections modulo the gauge group. Our first result shows that if such a moduli space is non-empty and the manifold admits a connected sum decomposition X ≅ X1 # X2, then both b2(X1) and b2(X2) are divisible by four; this rules out a previously naturally appearing source of 4-manifolds with non-empty moduli space. We give in some detail a construction of negative definite 4-manifolds which we expect will eventually provide examples of manifolds with non-empty moduli space.

Citation

Lobb, A., & Zentner, R. (2010). On Casson-type instanton moduli spaces over negative definite 4-manifolds. The Quarterly Journal of Mathematics, 62(2), 433-450. https://doi.org/10.1093/qmath/hap042

Journal Article Type Article
Publication Date Jan 13, 2010
Deposit Date Oct 18, 2011
Publicly Available Date Feb 14, 2014
Journal Quarterly Journal of Mathematics
Print ISSN 0033-5606
Electronic ISSN 1464-3847
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 62
Issue 2
Pages 433-450
DOI https://doi.org/10.1093/qmath/hap042

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Copyright Statement
This is a pre-copyedited author-produced PDF of an article accepted for publication in Quarterly journal of mathematics following peer review. The definitive publisher-authenticated version Lobb, Andrew and Zentner, Raphael (2010) 'On Casson-type instanton moduli spaces over negative definite 4-manifolds.', Quarterly journal of mathematics., 62 (2). pp. 433-450. is available online at: http://dx.doi.org/10.1093/qmath/hap042




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