On the Lê-Milnor fibration for real analytic maps
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- 作者：Auré ; lio Menegon Neto and José ; Seade
- 刊名：Mathematische Nachrichten
- 出版年：2017
- 出版时间：February 2017
- 年：2017
- 卷：290
- 期：2-3
- 页码：382-392
- 全文大小：211K
- ISSN：1522-2616
文摘
In this paper, we study the topology of real analytic map-germs with isolated critical value lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">f : lse">( le-struck">R m , 0 lse">) → lse">( le-struck">R n , 0 lse">) l:math>, with lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">1 < n < m l:math>. We compare the topology of f with the topology of the compositions lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">π i ∗ ∘ f l:math>, where lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">π i ∗ : le-struck">R n → le-struck">R n − 1 l:math> are the projections lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">lse">( t 1 , ⋯ , t n lse">) ↦ lse">( t 1 , ⋯ , t i − 1 , t i + 1 , ⋯ , t n lse">) l:math>, for lass="math-equation-construct">lass="math-equation-image">l="true" class="math-equation-mathml" style="display:none">l:math xmlns:mml="http://www.w3.org/1998/Math/MathML">lns:w="http://www.wiley.com/namespaces/wiley" xmlns:wiley="http://www.wiley.com/namespaces/wiley/wiley" xmlns:cr="urn://wiley-online-library/content/render" xmlns="http://www.w3.org/1998/Math/MathML">i = 1 , ⋯ , n l:math>. As a main result, we give necessary and sufficient conditions for f to have a Lê–Milnor fibration in the tube.