Four-manifolds up to connected sum with complex projective planes

Kaprowski, Daniel; Powell, Mark; Teichner, Peter

Abstract

Based on results of Kreck, we show that closed, connected 4- manifolds up to connected sum with copies of the complex projective plane are classified in terms of the fundamental group, the orientation character and an extension class involving the second homotopy group. For fundamental groups that are torsion free or have one end, we reduce this further to a classification in terms of the homotopy 2-type.

Citation

Kaprowski, D., Powell, M., & Teichner, P. (2022). Four-manifolds up to connected sum with complex projective planes. American Journal of Mathematics, 144(1), 75-118. https://doi.org/10.1353/ajm.2022.0001

• Journal Article Type: Article
• Acceptance Date: Jul 27, 2021
• Online Publication Date: Jan 13, 2022
• Publication Date: 2022-02
• Deposit Date: Mar 29, 2018
• Publicly Available Date: May 4, 2022
• Journal: American Journal of Mathematics
• Print ISSN: 0002-9327
• Electronic ISSN: 1080-6377
• Publisher: Johns Hopkins University Press
• Peer Reviewed: Peer Reviewed
• Volume: 144
• Issue: 1
• Pages: 75-118
• DOI: https://doi.org/10.1353/ajm.2022.0001
• Publisher URL: https://muse.jhu.edu/article/844459/pdf
• Related Public URLs: https://arxiv.org/abs/1802.09811