Abstract: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.
| Subjects: | K-Theory and Homology (math.KT) |
| Cite as: | arXiv:2605.24205 [math.KT] |
| (or arXiv:2605.24205v1 [math.KT] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24205 arXiv-issued DOI via DataCite (pending registration) |
From: Kyouhei Horie [view email]
[v1]
Fri, 22 May 2026 20:46:27 UTC (35 KB)
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