Complex sentence: The relation that two maps have the same r\\,-jet is an equivalence relation and the equivalence class with representative\\ sigma\\, is denoted j ^ --\\ sigma.
Split into simpler sentences: The relation that two maps have the same r-jet is an equivalence relation. An "r"-jet is an equivalence class under this relation, and the "r"-jet with representative\\ sigma\\, is denoted j ^ --\\ sigma.