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The Euler obstruction and the Chern obstruction:

Brasselet, J.-P. ; Grulha Jr., N. G. ; Ruas, M. A. S.
Bulletin of the London Mathematical Society.  42 (2010)  6 - p. 1035-1043 , 2010
Link: https://doi.org/10.1112/blms/bdq063