Second order homological obstructions on real algebraic manifolds

Ghiloni, Riccardo

doi:10.1016/j.topol.2007.07.003

Cited by 12 publications

(12 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, regular maps are often too rigid for such problems (cf. [5,7,8,9,11,13,14,18,19,20,27]). Continuous rational maps form a natural intermediate class be-tween regular and semi-algebraic maps, with many specific properties.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Approximation by continuous rational maps into spheres

Kucharz¹

2014

J. Eur. Math. Soc.

View full text Add to dashboard Cite

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Approximation by continuous rational maps into spheres

Kucharz¹

2014

J. Eur. Math. Soc.

View full text Add to dashboard Cite

show abstract

“…Topological properties of regular maps and their applications to algebraization of topological vector bundles were investigated in numerous papers [2][3][4][5][6][7][8][9][10][11][12][13][14][16][17][18][19][20][21][22][23][24][25]27,[32][33][34][35]37,38,[40][41][42][43][47][48][49]51,53,56,64,65,68,71,72,[76][77][78][79][80]82,83]. In gene...…”

Section: Introductionmentioning

confidence: 99%

Piecewise-regular maps

Kucharz

2017

Math. Ann.

View full text Add to dashboard Cite

Let V , W be real algebraic varieties (that is, up to isomorphism, real algebraic sets), and X ⊆ V some subset. A map from X into W is said to be regular if it can be extended to a regular map defined on some Zariski locally closed subvariety of V that contains X . Furthermore, a continuous map f : X → W is said to be piecewise-regular if there exists a stratification S of V such that for every stratum S ∈ S the restriction of f to each connected component of X ∩ S is a regular map. By a stratification of V we mean a finite collection of pairwise disjoint Zariski locally closed subvarieties whose union is equal to V . Assuming that the subset X of V is compact, we prove that every continuous map from X into a Grassmann variety or a unit sphere can be approximated by piecewise-regular maps. As an application, we obtain a variant of the algebraization theorem for topological vector bundles. If the variety V is compact and nonsingular, we prove that each continuous map from V into a unit sphere is homotopic to a piecewise-regular map of class C k , where k is an arbitrary nonnegative integer. Mathematics Subject Classification 14P05 · 14P99 · 57R22Communicated by Ngaiming Mok.

show abstract

“…This method is quite efficient since, as demonstrated by Theorem 2.1, the assumption that K be a boundary is not at all restrictive in applications. In particular, Theorem 2.8 is significantly sharper than Theorems 1.1, 1.1 , 1.2, 1.2 and 1.3 of [14] combined, whereas its proof is much simpler. Proof.…”

Section: ])mentioning

confidence: 93%