Milnor fibration at infinity

Singular open book structures from real mappings

“…in the local stratified setting as well as at infinity, see e.g. [15,[21][22][23] in order to produce locally trivial fibrations. See also [4].…”

Semi-algebraic neighborhoods of closed semi-algebraic sets

“…We will denote by Σ Proof. -As in [8, Lemma 1.8], we can prove using the curve selection lemma at infinity (see [21,Lemma 2]) that there exists a compact set K of R n such that ∇ρ 0 and ∇ρ 1 are non-zero and do not point in opposite direction outside K. Furthermore we can find r 1 > 0 such that for r r 1 , Σ is a non-empty compact C 2 hypersurface. To prove the second part of the lemma, we fix a non compact stratum S α of X.…”

Milnor fibrations of meromorphic functions

“…The following lemmas are easily obtained by adapting the proofs of Lemmas 4.3 and 4.4 in [8] as already performed in [9] and [1] in close situations.…”