Voir la notice de l'article provenant de la source Mathematical Sciences Publishers
We show that the integral equivariant cohomology Chern numbers completely determine the equivariant geometric unitary bordism classes of closed unitary G–manifolds, which gives an affirmative answer to a conjecture posed by Guillemin, Ginzburg and Karshon (Moment maps, cobordisms, and Hamiltonian group actions, Remark H.5 in Appendix H.3), where G is a torus. As a further application, we also obtain a satisfactory solution of their Question (A) (Appendix H.1.1) on unitary Hamiltonian G–manifolds. Our key ingredients in the proof are the universal toric genus defined by Buchstaber, Panov and Ray and the Kronecker pairing of bordism and cobordism. Our approach heavily exploits Quillen’s geometric interpretation of homotopic unitary cobordism theory. Moreover, this method can also be applied to the study of (ℤ2)k–equivariant unoriented bordism and can still derive the classical result of tom Dieck.
Keywords: equivariant unitary bordism, Hamiltonian bordism, equivariant cohomology Chern number
Lü, Zhi 1 ; Wang, Wei 2
@article{10_2140_agt_2018_18_4143,
author = {L\"u, Zhi and Wang, Wei},
title = {Equivariant cohomology {Chern} numbers determine equivariant unitary bordism for torus groups},
journal = {Algebraic and Geometric Topology},
pages = {4143--4160},
publisher = {mathdoc},
volume = {18},
number = {7},
year = {2018},
doi = {10.2140/agt.2018.18.4143},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.4143/}
}
TY - JOUR AU - Lü, Zhi AU - Wang, Wei TI - Equivariant cohomology Chern numbers determine equivariant unitary bordism for torus groups JO - Algebraic and Geometric Topology PY - 2018 SP - 4143 EP - 4160 VL - 18 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.4143/ DO - 10.2140/agt.2018.18.4143 ID - 10_2140_agt_2018_18_4143 ER -
%0 Journal Article %A Lü, Zhi %A Wang, Wei %T Equivariant cohomology Chern numbers determine equivariant unitary bordism for torus groups %J Algebraic and Geometric Topology %D 2018 %P 4143-4160 %V 18 %N 7 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.4143/ %R 10.2140/agt.2018.18.4143 %F 10_2140_agt_2018_18_4143
Lü, Zhi; Wang, Wei. Equivariant cohomology Chern numbers determine equivariant unitary bordism for torus groups. Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 4143-4160. doi: 10.2140/agt.2018.18.4143
Cité par Sources :