Geodesic
Formal groups and the Atiyah--Hirzebruch formula
Izvestiya. Mathematics , Tome 8 (1974) no. 6, pp. 1271-1285

Voir la notice de l'article provenant de la source Math-Net.Ru

In this article, manifolds with actions of compact Lie groups are considered. For each rational Hirzebruch genus $h\colon\Omega_*\to Q$, an “equivariant genus” $h^G$, a homomorphism from the bordism ring of $G$-manifolds to the ring $K(BG)\otimes Q$, is constructed. With the aid of the language of formal groups, for some genera it is proved that for a connected compact Lie group $G$, the image of $h^G$ belongs to the subring $Q\subset K(BG)\otimes Q$. As a consequence, extremely simple relations between the values of these genera on bordism classes of $S^1$-manifolds and submanifolds of its fixed points are found. In particular, a new proof of the Atiyah–Hirzebruch formula is obtained. 
@article{IM2_1974_8_6_a6,
     author = {I. M. Krichever},
     title = {Formal groups and the {Atiyah--Hirzebruch} formula},
     journal = {Izvestiya. Mathematics },
     pages = {1271--1285},
     publisher = {mathdoc},
     volume = {8},
     number = {6},
     year = {1974},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a6/}
}
TY  - JOUR
AU  - I. M. Krichever
TI  - Formal groups and the Atiyah--Hirzebruch formula
JO  - Izvestiya. Mathematics 
PY  - 1974
SP  - 1271
EP  - 1285
VL  - 8
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a6/
LA  - en
ID  - IM2_1974_8_6_a6
ER  - 
%0 Journal Article
%A I. M. Krichever
%T Formal groups and the Atiyah--Hirzebruch formula
%J Izvestiya. Mathematics 
%D 1974
%P 1271-1285
%V 8
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a6/
%G en
%F IM2_1974_8_6_a6
I. M. Krichever. Formal groups and the Atiyah--Hirzebruch formula. Izvestiya. Mathematics , Tome 8 (1974) no. 6, pp. 1271-1285. http://geodesic.mathdoc.fr/item/IM2_1974_8_6_a6/