Smooth structures on PL-manifolds of dimensions between 8 and 10

arXiv2302.02301MaRDI QIDQ6508695

Samik Basu, Priyanka Magar-Sawant, Ramesh Kasilingam

Abstract: In this paper, we identify the concordance classes of smooth structures on $PL$-manifolds of dimension between $8$ and $10$. Along the way, we compute the $k$-invariant of $PL/O$ until degree $10$. This leads to a computation of the homotopy inertia group. We verify in these cases that the concordance inertia group of a connected sum is the sum of the individual inertia groups. We also provide an explicit computation of the set of smooth structures up to concordance in some examples.

Mathematics Subject Classification ID

Homotopy equivalences in algebraic topology (55P10) Stable homotopy theory, spectra (55P42) Differentiable structures in differential topology (57R55) Cobordism and concordance in topological manifolds (57N70) Cobordism and concordance in PL-topology (57Q60)

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