= Exotic subset-cover class of a framed bundle
{title2=$l_k(\eta)=(p_k)_!(1)$}
= Exotic subset-cover classes of a framed bundle
{synonym}
The degree-zero <framed cobordism> class is defined by the transfer of the <subset cover of a framed vector bundle>. With the canonical relative framing it equals $\binom nk\cdot1$ for a globally ordered framing of rank $n$. Put $l_0=1$ and $l_k=0$ outside the rank range. Disjoint-union additivity and fiber-product multiplicativity of transfer give $l_k(\eta\oplus\zeta)=\sum_{i+j=k}l_i(\eta)l_j(\zeta)$.
Back to article page
