Nonzero alpha-invariant for every spin structure on a flat manifold

This paper addresses the Davis–Fang spin bordism question discussed in connection with Problem 17. It constructs a ten-dimensional closed flat Kähler manifold for which all 16 spin structures have alpha-invariant equal to 1. Each spin structure therefore represents a nonzero spin bordism class. This gives a negative answer to whether every almost flat spin manifold admits a spin structure that bounds a compact spin manifold. Repository: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometryPDF at the deposited version: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometry/blob/b4f17a71d1712073bf82196a01c29ae04292e5c1/papers/problem_17_spin_bordism.pdfTeX source at the deposited version: https://github.com/opensource120/Some-Answers-to-Yau-s-120-open-problems-in-geometry/blob/b4f17a71d1712073bf82196a01c29ae04292e5c1/papers/problem_17_spin_bordism.tex