Geodesic
An equivariant analog of the Poincar\'e--Hopf theorem
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 303-318

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A new method for localization of algebro-topological invariants of smooth manifolds is given in terms of equivariant tangent vector fields. Main realizations of direct image constructions – the Gysin map and the Becker–Gottlieb transfer map – are calculated for Grassmannizations of complex vector bundles and for a complex-oriented cohomology theory. 
@article{ZNSL_2000_267_a22,
     author = {K. E. Feldman},
     title = {An equivariant analog of the {Poincar\'e--Hopf} theorem},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {303--318},
     publisher = {mathdoc},
     volume = {267},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a22/}
}
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K. E. Feldman. An equivariant analog of the Poincar\'e--Hopf theorem. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 5, Tome 267 (2000), pp. 303-318. http://geodesic.mathdoc.fr/item/ZNSL_2000_267_a22/