On characteristic numbers of $24$ dimensional String manifolds
Algebraic Topology
2021-10-26 v3 Geometric Topology
Abstract
In this paper, we study the Pontryagin numbers of dimensional String manifolds. In particular, we find representatives of an integral basis of the String cobrodism group at dimension , based on the work of Mahowald-Hopkins \cite{MH02}, Borel-Hirzebruch \cite{BH58} and Wall \cite{Wall62}. This has immediate applications on the divisibility of various characteristic numbers of the manifolds. In particular, we establish the -primary divisibilities of the signature and of the modified signature coupling with the integral Wu class of Hopkins-Singer \cite{HS05}, and also the -primary divisibility of the twisted signature. Our results provide potential clues to understand a question of Teichner.
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Cite
@article{arxiv.2103.11413,
title = {On characteristic numbers of $24$ dimensional String manifolds},
author = {Fei Han and Ruizhi Huang},
journal= {arXiv preprint arXiv:2103.11413},
year = {2021}
}
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final version