تقرير
KSp-characteristic classes determine Spin$^h$ cobordism
| العنوان: | KSp-characteristic classes determine Spin$^h$ cobordism |
|---|---|
| المؤلفون: | Buchanan, Jonathan, McKean, Stephen |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Topology, Primary: 19L41. Secondary: 53C27 |
| الوصف: | A classic result of Anderson, Brown, and Peterson states that the cobordism spectrum MSpin (respectively, MSpin$^c$) splits as a sum of Eilenberg--Mac Lane spectra and connective covers of real K-theory (respectively, complex K-theory) at 2. We develop a theory of symplectic K-theory classes and use these to build an explicit splitting for MSpin$^h$ in terms of Eilenberg--Mac Lane spectra and spectra related to symplectic K-theory. This allows us to determine the Spin$^h$ cobordism groups systematically. We also prove that two Spin$^h$-manifolds are cobordant if and only if their underlying unoriented manifolds are cobordant and their KSp-characteristic numbers agree. Comment: 72 pages, 5 figures. Comments welcome! |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.08209 |
| رقم الأكسشن: | edsarx.2312.08209 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |