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- W2257679246 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 $M^{2n}$ be a closed $(n-1)$-connected $2n$-dimensional smooth manifold. We show that, for $n=4$, the homotopy inertia group of $M^{2n}$ is trivial and if $n=8$ and $H^n(M^{2n};mathbb{Z})cong mathbb{Z}$, the homotopy inertia group of $M^{2n}$ is also trivial. We further compute the group $mathcal{C}(M^{2n})$ of concordance classes of smoothings of $M^{2n}$ for $n=8$. Finally, we show that if a smooth manifold $N$ is tangentially homotopy equivalent to $M^8$, then $N$ is diffeomorphic to the connected sum of $M^8$ and a homotopy $8$-sphere." @default.
- W2257679246 created "2016-06-24" @default.
- W2257679246 creator A5063223599 @default.
- W2257679246 date "2015-11-12" @default.
- W2257679246 modified "2023-09-27" @default.
- W2257679246 title "Homotopy Inertia Groups and Tangential Structures" @default.
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