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On the Lê–Milnor fibration for real analytic maps
Author(s) -
Menegon Neto Aurélio,
Seade José
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201600066
Subject(s) - fibration , mathematics , topology (electrical circuits) , pure mathematics , combinatorics , homotopy
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.