3 problems

Let $(\Theta,\Phi)$ be a tangential pair, let $F$ be the fibre of $\Theta \to \Phi$, let $A$ be the Thom ring spectrum of the index bundle over $\Omega F$, and let $R$ be the Thom…

Let $(\Theta,\Phi)$ be a tangential pair, meaning based spaces equipped with maps fitting into a commutative diagram over $BO \to BU$. Let $X$ admit a $\Phi$-structure, set…

Let $X$ be a Liouville domain with stable tangent bundle classified by $X \to BU$, and let $\Phi \to BU$ be a based space over $BU$. Suppose the classifying map $X \to BU$ factors…