Odd Koschorke classes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866913157895684096 |
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| author | Horie, Kyouhei |
| author_facet | Horie, Kyouhei |
| contents | We introduce odd Koschorke classes in odd K-theory by using degeneracy loci of self-adjoint Fredholm operators. These classes are characteristic classes analogous to the even Koschorke classes in even K-theory. We study two aspects of these classes: their role as obstruction classes and their realization as characteristic classes with real coefficients for odd twisted K-theory. On the even side, we introduce generalized Koschorke classes indexed by arbitrary partitions via Cibotaru's notion of a quasi-manifold. These classes form a \(\mathbb{C}\)-basis of \(H^*(\mathrm{Fred}_0;\mathbb{C})\) and recover the usual Koschorke classes for rectangular partitions. Finally, by analogy with the correspondence between even Koschorke classes and singular vectors for a representation of the Virasoro algebra, we state a result for a representation of a super-Virasoro algebra: each singular vector has a unique finite expansion in terms of generalized Koschorke classes and generalized odd Koschorke classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24205 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Odd Koschorke classes Horie, Kyouhei K-Theory and Homology We introduce odd Koschorke classes in odd K-theory by using degeneracy loci of self-adjoint Fredholm operators. These classes are characteristic classes analogous to the even Koschorke classes in even K-theory. We study two aspects of these classes: their role as obstruction classes and their realization as characteristic classes with real coefficients for odd twisted K-theory. On the even side, we introduce generalized Koschorke classes indexed by arbitrary partitions via Cibotaru's notion of a quasi-manifold. These classes form a \(\mathbb{C}\)-basis of \(H^*(\mathrm{Fred}_0;\mathbb{C})\) and recover the usual Koschorke classes for rectangular partitions. Finally, by analogy with the correspondence between even Koschorke classes and singular vectors for a representation of the Virasoro algebra, we state a result for a representation of a super-Virasoro algebra: each singular vector has a unique finite expansion in terms of generalized Koschorke classes and generalized odd Koschorke classes. |
| title | Odd Koschorke classes |
| topic | K-Theory and Homology |
| url | https://arxiv.org/abs/2605.24205 |