On the Lê–Milnor fibration for real analytic maps

In this paper, we study the topology of real analytic map‐germs with isolated critical value f : ( R m , 0 ) → ( R n , 0 ) , with 1 < n < m . We compare the topology of f with the topology of the compositionsπ i ∗ ∘ f , whereπ i ∗ : R n → R n − 1are the projections( t 1 , ⋯ , t n ) ↦ ( t 1 , ⋯ , t i − 1 , t i + 1 , ⋯ , t n ) , for i = 1 , ⋯ , n . As a main result, we give necessary and sufficient conditions for f to have a Lê–Milnor fibration in the tube.