"Homotopy inertia groups and tangential structures" by Ramesh Kasilingam
 

Homotopy inertia groups and tangential structures

Article Type

Research Article

Publication Title

JP Journal of Geometry and Topology

Abstract

We show that if M and N have the same homotopy type of simply connected closed smooth m-manifolds such that the integral and mod-2 cohomologies of M vanish in odd degrees, then their homotopy inertia groups are equal. Let M2n be a closed (n − 1) -connected 2n-dimensional smooth manifold. We show that, for n = 4, the homotopy inertia group of M2n is trivial and if n = 8 and Hn( M2n; Z) ~= Z, then the homotopy inertia group of M2n is also trivial. We further compute the group C (M2n) of concordance classes of smoothings of M2n for n = 8. Finally, we show that if a smooth manifold N is tangentially homotopy equivalent to M8, then N is diffeomorphic to the connected sum of M8 and a homotopy 8-sphere.

First Page

91

Last Page

114

DOI

10.17654/GT020020091

Publication Date

1-1-2017

Comments

Open Access, Green

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