A fibration with a section and of infinite genus (Q1840639)

The genus of a fibration \(p:E\to B\) is the least integer that \(B\) can be covered by \(n+1\) open sets over each of which \(p\) is trivial. In the case when \(p\) is a principal \(G\)-bundle, the genus can be defined in terms of sections: It is the least integer that \(B\) can be covered by \(n+1\) open sets over each of which \(p\) admits a section. The author shows that for a general fibration this is not true. Using Sullivan's model theory, he constructs a fibration with infinite genus which admits a section.