TY - JOUR

T1 - On the Chern–Losik Number of Codimension 2 Foliations

AU - Efremenko, Yu D.

N1 - The work was supported by the Mathematical Center in Akademgorodok under agreement 075–15–2025–349 with the Ministry of Science and Higher Education of the Russian Federation. Efremenko, Yu. D. On the Chern–Losik Number of Codimension $ 2 $ Foliations / Yu. D. Efremenko // Siberian Mathematical Journal. – 2025. – Vol. 66, No. 5. – P. 1158-1170. – DOI 10.1134/S0037446625050064.

PY - 2025/9/30

Y1 - 2025/9/30

N2 - We study the first Chern–Losik class of codimension foliations on bundles over the circle whose structure group is a cyclic subgroup of the special linear group over the field of complex numbers.We introduce the notion of the Chern–Losik number for foliations having at least two hyperbolic leaves.It is shown that for matrices conjugate to diagonal matrices with distinct diagonal entries whose moduli are different from one, the Chern–Losik class of the corresponding foliation is nontrivial.In this case the value of the Chern–Losik numberis uniquely determined by the diagonal entries.For matrices conjugate to diagonal matrices with distinct diagonal entries of modulus one, the Chern–Losik class is trivial.For matrices conjugate to the identity matrix, the Chern–Losik class is trivial, while for matrices conjugate to a Jordan block it is nontrivial.

AB - We study the first Chern–Losik class of codimension foliations on bundles over the circle whose structure group is a cyclic subgroup of the special linear group over the field of complex numbers.We introduce the notion of the Chern–Losik number for foliations having at least two hyperbolic leaves.It is shown that for matrices conjugate to diagonal matrices with distinct diagonal entries whose moduli are different from one, the Chern–Losik class of the corresponding foliation is nontrivial.In this case the value of the Chern–Losik numberis uniquely determined by the diagonal entries.For matrices conjugate to diagonal matrices with distinct diagonal entries of modulus one, the Chern–Losik class is trivial.For matrices conjugate to the identity matrix, the Chern–Losik class is trivial, while for matrices conjugate to a Jordan block it is nontrivial.

KW - 514.7

KW - Chern–Losik class

KW - Gelfand–Fuchs cohomology

KW - characteristic classes of foliations

KW - dynamical systems

KW - fixed points

KW - foliation

KW - leaf space

UR - https://www.mendeley.com/catalogue/169d2cf2-e7b6-3463-b905-ec6947de798e/

UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105017660696&origin=inward

U2 - 10.1134/S0037446625050064

DO - 10.1134/S0037446625050064

M3 - Article

VL - 66

SP - 1158

EP - 1170

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -