Aspherical 4-manifolds of odd Euler characteristic

Edmonds, Allan

doi:10.1090/proc/14675

Aspherical 4-manifolds of odd Euler characteristic
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by Allan L. Edmonds PDF

Proc. Amer. Math. Soc. 148 (2020), 421-434 Request permission

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.

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