Geodesic
Calculation of Hirzebruch genera for manifolds acted on by the group $\mathbf Z/p$ via invariants of the action
Izvestiya. Mathematics , Tome 62 (1998) no. 3, pp. 515-548.

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

We obtain general formulae expressing Hirzebruch genera of a manifold with $\mathbf Z/p$-action in terms of invariants of this action (the sets of weights of fixed points). As an illustration, we consider numerous particular cases of well-known genera, in particular, the elliptic genus. We also describe the connection with the so-called Conner–Floyd equations for the weights of fixed points. 
@article{IM2_1998_62_3_a3,
     author = {T. E. Panov},
     title = {Calculation of {Hirzebruch} genera for manifolds acted on by the group $\mathbf Z/p$ via invariants of the action},
     journal = {Izvestiya. Mathematics },
     pages = {515--548},
     publisher = {mathdoc},
     volume = {62},
     number = {3},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a3/}
}
TY  - JOUR
AU  - T. E. Panov
TI  - Calculation of Hirzebruch genera for manifolds acted on by the group $\mathbf Z/p$ via invariants of the action
JO  - Izvestiya. Mathematics 
PY  - 1998
SP  - 515
EP  - 548
VL  - 62
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a3/
LA  - en
ID  - IM2_1998_62_3_a3
ER  - 
%0 Journal Article
%A T. E. Panov
%T Calculation of Hirzebruch genera for manifolds acted on by the group $\mathbf Z/p$ via invariants of the action
%J Izvestiya. Mathematics 
%D 1998
%P 515-548
%V 62
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a3/
%G en
%F IM2_1998_62_3_a3
T. E. Panov. Calculation of Hirzebruch genera for manifolds acted on by the group $\mathbf Z/p$ via invariants of the action. Izvestiya. Mathematics , Tome 62 (1998) no. 3, pp. 515-548. http://geodesic.mathdoc.fr/item/IM2_1998_62_3_a3/

[1] Atya M., Bott R., “Zametki o teoreme Lefshetsa o nepodvizhnoi tochke”, Matematika, 10:4 (1966), 101–139

[2] Bott R., Taubes C., “On the rigidity theorems of Witten”, J. of Amer. Math. Soc., 2 (1989), 137–186 | DOI | MR | Zbl

[3] Atya M., Zinger I., “Indeks ellipticheskikh operatorov, III”, UMN, 24:1(145) (1969), 127–182 | MR

[4] Bukhshtaber V. M., “Kharakter Chzhenya–Dolda v teorii kobordizmov, I”, Matem. sb., 83:4 (1970), 575–595 | MR | Zbl

[5] Bukhshtaber V. M., Novikov S. P., “Formalnye gruppy, stepennye sistemy i operatory Adamsa”, Matem. sb., 84:1 (1971), 81–118 | MR | Zbl

[6] Khirtsebrukh F., Topologicheskie metody v algebraicheskoi geometrii, Mir, M., 1973

[7] Hirzebruch F., Berger T., Jung R., Manifolds and Modular Forms, Second Edition, Max-Planc-Institut für Mathematik, Bonn, 1994

[8] Kasparov G. G., “Invarianty klassicheskikh linzovykh mnogoobrazii v teorii kobordizmov”, Izv. AN SSSR. Ser. matem., 33:4 (1969), 735–747 | MR | Zbl

[9] Krichever I. M., “Obobschennye ellipticheskie rody i funktsii Beikera–Akhiezera”, Matem. zametki, 47:2 (1990), 34–45 | MR

[10] Elliptic Curves and Modular Forms in Algebraic Topology, Lecture Notes in Mathematics, 1326, ed. P. S. Landweber, Springer, Berlin–Heidelberg, 1988 | MR

[11] Mischenko A. S., “Mnogoobraziya s deistviem gruppy $\mathbf Z_p$ i nepodvizhnye tochki”, Matem. zametki, 4:4 (1968), 381–386 | MR | Zbl

[12] Novikov S. P., “Metody algebraicheskoi topologii s tochki zreniya teorii kobordizmov”, Izv. AN SSSR. Ser. matem., 31:4 (1967), 855–951 | MR | Zbl

[13] Novikov S. P., “Operatory Adamsa i nepodvizhnye tochki”, Izv. AN SSSR. Ser. matem., 32:6 (1968), 1245–1263 | MR

[14] Ochanine S., “Sur les genres multiplicatifs définis par des intégrales elliptiques”, Topology, 26 (1987), 143–151 | DOI | MR | Zbl

[15] Panov T. E., “Ellipticheskii rod dlya mnogoobrazii s deistviem gruppy $\mathbb Z/p$”, UMN, 52:2 (1997), 181–182 | MR | Zbl