• Corpus ID: 207795537

# On the boundaries of highly connected, almost closed manifolds

@article{Burklund2019OnTB,
title={On the boundaries of highly connected, almost closed manifolds},
author={Robert Burklund and Jeremy Hahn and Andrew Senger},
journal={arXiv: Algebraic Topology},
year={2019}
}
• Published 30 October 2019
• Mathematics
• arXiv: Algebraic Topology
Building on work of Stolz, we prove for integers $0 \le d \le 3$ and $k>232$ that the boundaries of $(k-1)$-connected, almost closed $(2k+d)$-manifolds also bound parallelizable manifolds. Away from finitely many dimensions, this settles longstanding questions of C.T.C. Wall, determines all Stein fillable homotopy spheres, and proves a conjecture of Galatius and Randal--Williams. Implications are drawn for both the classification of highly connected manifolds and, via work of Krannich and Kreck…

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