On parallelizability and span of the Dold manifolds (Q2839377)

This well written paper studies the Dold manifolds \(P(m,n)\), which are defined as the quotient space of \(S^n \times \mathbb CP^n\) using the involution which is the antipodal map on the sphere and complex conjugation on the complex projective space. The author characterizes the stably parallelizable Dold manifolds. There are only six given by the set of pairs below for which \((m,n) \in \{ (1,0), (3,0) (7,0), (0,1), (2,1), (6,1) \} \). The first three of the set of six are also the only parellelizable Dold manifolds.NEWLINENEWLINEThe author also studies the span of \(P(m,1)\). Novotný determined the span for all \(m\) except for \(m \neq 15 (mod 16)\) The author completes the classification by proving in that case that the span is zero for even \(m\), and for odd \(m\), \(span(P(m,1))= 1+span(S^m) = 2^c + 8d\), where \(m + 1=\)(odd number)\(\times 2^{c + 4d}\).