SU$-linear operations in complex cobordism and the $c_1$-spherical bordism theory
We study the $SU$-linear operations in complex cobordism and prove that they are generated by the well-known geometric operations $\partial_i$. For the theory $W$ of $c_1$-spherical bordism, we describe all $SU$-linear multiplications on $W$ and projections $MU \to W$. We also analyse complex orient...
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Veröffentlicht in: | Izvestiya. Mathematics 2023, Vol.87 (4), p.768-797 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | We study the $SU$-linear operations in complex cobordism and prove that
they are generated by the well-known geometric operations $\partial_i$.
For the theory $W$ of $c_1$-spherical bordism, we describe all
$SU$-linear multiplications on $W$ and projections $MU \to W$. We also
analyse complex orientations on $W$ and the corresponding formal group
laws $F_W$. The relationship between the formal group laws $F_W$
and the coefficient ring $W_*$ of the $W$-theory was studied
by Buchstaber in 1972. We extend his results by showing that for any
$SU$-linear multiplication and orientation on $W$, the coefficients
of the corresponding formal group law $F_W$ do not generate the ring $W_*$,
unlike the situation with complex bordism. |
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ISSN: | 1064-5632 1468-4810 |
DOI: | 10.4213/im9334e |