Geodesic
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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@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
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/

[1] J.-L. Brylinski, Loop Spaces, Characteristic Classes and Geometric Quantization, Birkhäuser, Basel, 2008 | MR | Zbl

[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