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On Local Combinatorial Formulas for Chern Classes of a Triangulated Circle Bundle. / Mnev, N.; Sharygin, G.
в: Journal of Mathematical Sciences (United States), Том 224, № 2, 01.07.2017, стр. 304-327.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - On Local Combinatorial Formulas for Chern Classes of a Triangulated Circle Bundle
AU - Mnev, N.
AU - Sharygin, G.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - A principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklace (in the combinatorial sense). We express rational local formulas for all powers of the first Chern class in terms of expectations of the parities of the associated necklaces. This rational parity is a combinatorial isomorphism invariant of a triangulated circle bundle over a simplex, measuring the mixing by the triangulation of the circular graphs over vertices of the simplex. The goal of this note is to sketch the logic of deducing these formulas from Kontsevitch’s cyclic invariant connection form on metric polygons.
AB - A principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a simplex we associate a necklace (in the combinatorial sense). We express rational local formulas for all powers of the first Chern class in terms of expectations of the parities of the associated necklaces. This rational parity is a combinatorial isomorphism invariant of a triangulated circle bundle over a simplex, measuring the mixing by the triangulation of the circular graphs over vertices of the simplex. The goal of this note is to sketch the logic of deducing these formulas from Kontsevitch’s cyclic invariant connection form on metric polygons.
UR - http://www.scopus.com/inward/record.url?scp=85019686152&partnerID=8YFLogxK
U2 - 10.1007/s10958-017-3416-2
DO - 10.1007/s10958-017-3416-2
M3 - Article
AN - SCOPUS:85019686152
VL - 224
SP - 304
EP - 327
JO - Journal of Mathematical Sciences
JF - Journal of Mathematical Sciences
SN - 1072-3374
IS - 2
ER -
ID: 126276893