On the generalized brace product: relation to $H$-splitting of loop space fibrations \& the $J$-homomorphism

Somnath Basu, Aritra Bhowmick, Sandip Samanta

Given a fibration $F\hookrightarrow E\to B$ with a homotopy section $s:B\to E$, James introduced a binary product $\left\{, \right\}_s: π_i B \times π_j F \ri…