On the index of principal foliations of surfaces in R^3 with corank 1 singularities
Journal of Singularities, Tome 22 (2020), pp. 1-16
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It is well known that the index associated to the principal foliations at a cross-cap point is 1/2. In this work we study the index for other corank 1 singularities from (R^2,0) to (R^3,0) which either are simple or are non-simple but included in strata of A_e-codimension ≤ 3. We show that the index, under certain conditions, is always 0 or 1, bearing out that the Loewner conjecture could be true for all corank 1 singularities.
@article{10_5427_jsing_2020_22a,
author = {J. C. F. Costa and L. F. Martins, and J. J. Nu\~no-Ballesteros},
title = {On the index of principal foliations of surfaces in {R^3} with corank 1 singularities},
journal = {Journal of Singularities},
pages = {1--16},
publisher = {mathdoc},
volume = {22},
year = {2020},
doi = {10.5427/jsing.2020.22a},
url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.22a/}
}
TY - JOUR AU - J. C. F. Costa AU - L. F. Martins, AU - J. J. Nuño-Ballesteros TI - On the index of principal foliations of surfaces in R^3 with corank 1 singularities JO - Journal of Singularities PY - 2020 SP - 1 EP - 16 VL - 22 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.22a/ DO - 10.5427/jsing.2020.22a ID - 10_5427_jsing_2020_22a ER -
%0 Journal Article %A J. C. F. Costa %A L. F. Martins, %A J. J. Nuño-Ballesteros %T On the index of principal foliations of surfaces in R^3 with corank 1 singularities %J Journal of Singularities %D 2020 %P 1-16 %V 22 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.5427/jsing.2020.22a/ %R 10.5427/jsing.2020.22a %F 10_5427_jsing_2020_22a
J. C. F. Costa; L. F. Martins,; J. J. Nuño-Ballesteros. On the index of principal foliations of surfaces in R^3 with corank 1 singularities. Journal of Singularities, Tome 22 (2020), pp. 1-16. doi: 10.5427/jsing.2020.22a
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