Elliptic genus and string cobordism at dimension $24$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2021
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910427556872192 |
|---|---|
| author | Han, Fei Huang, Ruizhi |
| author_facet | Han, Fei Huang, Ruizhi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_11022 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Elliptic genus and string cobordism at dimension $24$ Han, Fei Huang, Ruizhi Algebraic Topology Differential Geometry Geometric Topology 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. |
| title | Elliptic genus and string cobordism at dimension $24$ |
| topic | Algebraic Topology Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2110.11022 |