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

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 ${\Omega }^W$ 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 ${\Omega }^W$, unlike the situation with complex bordism.

25 pages, published version

References in corpus (2)

• SU-bordism: structure results and geometric representatives
• Polynomial generators of msu*[1/2] related to classifying maps of certain formal group laws

Cited by in corpus (1)

• Polynomial generators of msu*[1/2] related to classifying maps of certain formal group laws