Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 75-81
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N. E. Mnëv. Which circle bundles can be triangulated over $\partial\Delta^3$?. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIX, Tome 468 (2018), pp. 75-81. http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a6/
@article{ZNSL_2018_468_a6,
author = {N. E. Mn\"ev},
title = {Which circle bundles can be triangulated over~$\partial\Delta^3$?},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {75--81},
year = {2018},
volume = {468},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a6/}
}
TY - JOUR
AU - N. E. Mnëv
TI - Which circle bundles can be triangulated over $\partial\Delta^3$?
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2018
SP - 75
EP - 81
VL - 468
UR - http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a6/
LA - en
ID - ZNSL_2018_468_a6
ER -
%0 Journal Article
%A N. E. Mnëv
%T Which circle bundles can be triangulated over $\partial\Delta^3$?
%J Zapiski Nauchnykh Seminarov POMI
%D 2018
%P 75-81
%V 468
%U http://geodesic.mathdoc.fr/item/ZNSL_2018_468_a6/
%G en
%F ZNSL_2018_468_a6
We prove that having the boundary of the standard three-dimensional simplex $\partial\Delta^3$ as the base of a triangulation, one can triangulate only trivial and Hopf circle bundles.
[2] S. Chern, “Circle bundles”, Lect. Notes Math., 597, 1977, 114–131 | DOI | MR | Zbl
[3] G. Gangopadhyay, Counting triangles formula for the first Chern class of a circle bundle, 2017, arXiv: 1712.03024
[4] K. V. Madahar, “Simplicial maps from the $3$-sphere to the $2$-sphere”, Adv. Geom., 2:2 (2002), 99–106 | DOI | MR | Zbl
[5] K. V. Madahar, K. S. Sarkaria, “A minimal triangulation of the Hopf map and its application”, Geom. Dedicata, 82:1–3 (2000), 105–114 | DOI | MR | Zbl
[6] N. Mnëv, G. Sharygin, “On local combinatorial formulas for Chern classes of a triangulated circle bundle.”, J. Math. Sci., 224:2 (2017), 304–327 | DOI | MR | Zbl