On the Euler characteristics of real Milnor fibres of partially parallelizable maps of (R<sup>
 n
</sup>, 0) to (R<sup>2</sup>, 0)

Dutertre, Nicolas

On the Euler characteristics of real Milnor fibres of partially parallelizable maps of (Rⁿ, 0) to (R², 0)

Kodai Math. J., Tome 32 (2009) no. 1, p. 324-351 / Harvested from Project Euclid

Résumé

We consider a real analytic map-germ (f, g):(Rⁿ,0) → (R²,0) such that the fibres of f are simultaneously parallelizable. We call such a map a partially parallelizable map. We establish degree formulas for the following quantities: ¶ χ ({f = α} $cap$ {g = δ} $cap$ B_εⁿ), ¶ χ ({f = α} $cap$ {g ≥ δ} $cap$ B_εⁿ) − χ ({f = α} $cap$ {g ≤ δ} $cap$ B_εⁿ), ¶ where (α, δ) is a regular value of (f, g) and 0 < |(α, δ)| « ε « 1.

Publié le : 2009-06-15
Classification:

@article{1245982908,
     author = {Dutertre, Nicolas},
     title = {On the Euler characteristics of real Milnor fibres of partially parallelizable maps of (R<sup>
 n
</sup>, 0) to (R<sup>2</sup>, 0)},
     journal = {Kodai Math. J.},
     volume = {32},
     number = {1},
     year = {2009},
     pages = { 324-351},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1245982908}
}

Dutertre, Nicolas. On the Euler characteristics of real Milnor fibres of partially parallelizable maps of (Rⁿ, 0) to (R², 0). Kodai Math. J., Tome 32 (2009) no. 1, pp.  324-351. http://gdmltest.u-ga.fr/item/1245982908/