Aspherical 4-manifolds of odd Euler characteristic
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- by Allan L. Edmonds PDF
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Abstract:
An explicit construction of closed, orientable, smooth, aspherical 4-manifolds with any odd Euler characteristic greater than 12 is presented. The constructed manifolds are all Haken manifolds in the sense of B. Foozwell and H. Rubinstein and can be systematically reduced to balls by suitably cutting them open along essential codimension-one submanifolds. Euler characteristics divisible by 3 are known to arise from complex algebraic geometry considerations. Examples with Euler characteristic 1, 5, 7, or 11 appear to be unknown.References
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Additional Information
- Allan L. Edmonds
- Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
- MR Author ID: 61840
- Email: edmonds@indiana.edu
- Received by editor(s): October 5, 2018
- Received by editor(s) in revised form: March 28, 2019
- Published electronically: June 14, 2019
- Communicated by: Ken Bromberg
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 421-434
- MSC (2010): Primary 57N13; Secondary 57N65
- DOI: https://doi.org/10.1090/proc/14675
- MathSciNet review: 4042863