Email this article An elementary approach to local combinatorial formulae for the Euler class of a PL spherical fiber bundle
- Authors: Panina G.Y.1
-
Affiliations:
- St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 214, No 3 (2023)
- Pages: 153-168
- Section: Articles
- URL: https://ogarev-online.ru/0368-8666/article/view/133527
- DOI: https://doi.org/10.4213/sm9737
- ID: 133527
Cite item
Open Access
Access granted
Subscription Access
Abstract
We present an elementary approach to local combinatorial formulae for the Euler class of a fibre-oriented triangulated spherical fibre bundle. This approach is based on sections averaging technique and very basic knowledge of simplicial (co)homology theory. Our formulae are close relatives of those due to Mnëv.
About the authors
Gaiane Yur'evna Panina
St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences
Author for correspondence.
Email: gaiane-panina@rambler.ru
Doctor of physico-mathematical sciences, no status
References
- N. Mnev, G. Sharygin, “On local combinatorial formulas for Chern classes of a triangulated circle bundle”, Теория представлений, динамические системы, комбинаторные методы. XXVII, Зап. науч. сем. ПОМИ, 448, ПОМИ, СПб., 2016, 201–235
- K. Igusa, “Combinatorial Miller–Morita–Mumford classes and Witten cycles”, Algebr. Geom. Topol., 4:1 (2004), 473–520
- N. E. Mnëv, “A note on a local combinatorial formula for the Euler class of a PL spherical fiber bundle”, Теория представлений, динамические системы, комбинаторные методы. XXXIII, Зап. науч. сем. ПОМИ, 507, ПОМИ, СПб., 2021, 35–58
- M. È. Kazarian, “The Chern–Euler number of circle bundle via singularity theory”, Math. Scand., 82:2 (1998), 207–236
- G. Gangopadhyay, Counting triangles formula for the first Chern class of a circle bundle
- Дж. Милнор, Дж. Сташеф, Характеристические классы, Мир, М., 1979, 371 с.
- Д. Б. Фукс, А. Т. Фоменко, В. Л. Гутенмахер, Гомотопическая топология, Изд-во Моск. ун-та, М., 1969, 459 с.
- B. Eckman, “Harmonische Funktionen und Randwertaufgaben in einem Komplex”, Comment. Math. Helv., 17 (1945), 240–255
- Д. А. Городков, Комбинаторное вычисление первого класса Понтрягина и приложения, Дисс. … канд. физ.-матем. наук, МИАН, М., 2021, 88 с.
Supplementary files
