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This article is cited in 3 scientific papers (total in 3 papers)
Generators of $S^1$-bordism
O. R. Musin
Abstract:
In this paper generators are found for the rings $U^{S^1}_*$ (the unitary $S^1$-bordism ring) and $U_*(S^1,\{\mathbf Z_s\})$ (the unitary bordism ring with actions of the group $S^1$ without fixed points). The generators found are $S^1$-manifolds of the form $(S^3)^k\times\mathbf CP^n/(S^1)^k$. By an obvious construction the ring $U^{S^1}_*$ allows one to establish a relation between numerical invariants of manifolds with unitary actions of $S^1$ and the set of fixed points, without using a theorem of the type of an integrality theorem. In particular, we obtain a new proof of the Atiyah–Hirzebruch formula for the generalized Todd genus of $S^1$-manifolds.
Bibliography: 9 titles.
Received: 22.09.1980
Citation:
O. R. Musin, “Generators of $S^1$-bordism”, Mat. Sb. (N.S.), 116(158):3(11) (1981), 359–369; Math. USSR-Sb., 44:3 (1983), 325–334
Linking options:
https://www.mathnet.ru/eng/sm2473https://doi.org/10.1070/SM1983v044n03ABEH000970 https://www.mathnet.ru/eng/sm/v158/i3/p359
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Abstract page: | 247 | Russian version PDF: | 98 | English version PDF: | 9 | References: | 43 |
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