Landweber exactness of the formal group law in $c_1$-spherical bordism

Abstract

We describe the structure of the coefficient ring $W^{\ast }(pt)={\Omega }_W^{\ast }$ of the $c_1$-spherical bordism theory for an arbitrary $SU$-bilinear multiplication. We prove that for any $SU$-bilinear multiplication the formal group of the theory $W^{\ast }$ is Landweber exact. Also we show that after inverting the set $\mathcal{P}$ of Fermat primes there exists a complex orientation of the localized theory $W^{\ast }[{\mathcal{P}}^{-1}]$ such that the coefficients of the corresponding formal group law generate the whole coefficient ring ${\Omega }_W^{\ast }[{\mathcal{P}}^{-1}]$.