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arXiv · 2110.11022

Elliptic genus and string cobordism at dimension $24$

Fei Han·Ruizhi Huang
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Abstract

It is known that spin cobordism can be determined by Stiefel-Whitney numbers and index theory invariants, namely $KO$-theoretic Pontryagin numbers. In this paper, we show that string cobordism at dimension 24 can be determined by elliptic genus, a higher index theory invariant. We also compute the image of 24 dimensional string cobordism under elliptic genus. Using our results, we show that under certain curvature conditions, a compact 24 dimensional string manifold must bound a string manifold.

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Fei Han, Ruizhi Huang. 2021-10-21. Elliptic genus and string cobordism at dimension $24$. https://doi.org/10.2140/pjm.2024.328.275

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