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arXiv · 2106.11876

$SU$-linear operations in complex cobordism and the $c_1$-spherical bordism theory

Georgy Chernykh·Taras Panov
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Abstract

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 $\varOmega^W$ 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 $\varOmega^W$, unlike the situation with complex bordism.

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Georgy Chernykh, Taras Panov. 2021-06-22. $SU$-linear operations in complex cobordism and the $c_1$-spherical bordism theory. https://doi.org/10.4213/im9334

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