• Corpus ID: 207795537

On the boundaries of highly connected, almost closed manifolds

  title={On the boundaries of highly connected, almost closed manifolds},
  author={Robert Burklund and Jeremy Hahn and Andrew Senger},
  journal={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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