Volume 8, issue 1 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
The Jacobi orientation and the two-variable elliptic genus

Matthew Ando, Christopher P French and Nora Ganter

Algebraic & Geometric Topology 8 (2008) 493–539
1 J F Adams, Stable homotopy and generalised homology, Univ. of Chicago Press (1974) MR0402720
2 M Ando, The sigma orientation for analytic circle-equivariant elliptic cohomology, Geom. Topol. 7 (2003) 91 MR1988282
3 M Ando, M Basterra, The Witten genus and equivariant elliptic cohomology, Math. Z. 240 (2002) 787 MR1922730
4 M Ando, J Greenlees, Circle-equivariant classifying spaces and the rational equivariant sigma genus arXiv:abs/0705.2687
5 M Ando, M J Hopkins, N P Strickland, Elliptic spectra, the Witten genus and the theorem of the cube, Invent. Math. 146 (2001) 595 MR1869850
6 L Borisov, A Libgober, Elliptic genera of singular varieties, orbifold elliptic genus and chiral de Rham complex, from: "Mirror symmetry, IV (Montreal, QC, 2000)", AMS/IP Stud. Adv. Math. 33, Amer. Math. Soc. (2002) 325 MR1969036
7 L Borisov, A Libgober, Elliptic genera of singular varieties, Duke Math. J. 116 (2003) 319 MR1953295
8 L Borisov, A Libgober, McKay correspondence for elliptic genera, Ann. of Math. $(2)$ 161 (2005) 1521 MR2180406
9 L Breen, Fonctions thêta et théorème du cube, Lecture Notes in Mathematics 980, Springer (1983) MR823233
10 R L Cohen, J D S Jones, G B Segal, Floer's infinite-dimensional Morse theory and homotopy theory, from: "The Floer memorial volume", Progr. Math. 133, Birkhäuser (1995) 297 MR1362832
11 P Deligne, Courbes elliptiques: formulaire d'après J. Tate, from: "Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)", Lecture Notes in Math. 476, Springer (1975) 53 MR0387292
12 P Deligne, M Rapoport, Les schémas de modules de courbes elliptiques, from: "Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)", Springer (1973) MR0337993
13 R Dijkgraaf, G Moore, E Verlinde, H Verlinde, Elliptic genera of symmetric products and second quantized strings, Comm. Math. Phys. 185 (1997) 197 MR1463039
14 E Dyer, Cohomology theories, Mathematics Lecture Note Series, W. A. Benjamin, New York-Amsterdam (1969) MR0268883
15 H. Eguchi, H. Ooguri, A. Taormina, S K Yang, Superconformal algebras and string compactification on manifolds with ${S}{U}({N})$ holonomy, Nucl. Phys. B 315 (1989) 193
16 M Eichler, D Zagier, The theory of Jacobi forms, Progress in Mathematics 55, Birkhäuser (1985) MR781735
17 N Ganter, Orbifold genera, product formulas and power operations, Adv. Math. 205 (2006) 84 MR2254309
18 J P C Greenlees, Rational $S^1$–equivariant elliptic cohomology, Topology 44 (2005) 1213 MR2168575
19 J P C Greenlees, J P May, Generalized Tate cohomology, Mem. Amer. Math. Soc. 113 (1995) MR1230773
20 I Grojnowski, Delocalized equivariant elliptic cohomology, from: "Elliptic cohomology" (editors H R Miller, D C Ravenel), London Math. Society Lecture Note Series 342, Cambridge University Press (2007) MR2330502
21 F Hirzebruch, Elliptic genera of level $N$ for complex manifolds, from: "Differential geometrical methods in theoretical physics (Como, 1987)", NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 250, Kluwer Acad. Publ. (1988) 37 MR981372
22 F Hirzebruch, T Berger, R Jung, Manifolds and modular forms, Aspects of Mathematics E20, Friedr. Vieweg & Sohn (1992) MR1189136
23 G Höhn, Komplexe elliptische Geschlechter und ${S}^1$–äquivariante Kobordimustheorie (complex elliptic genera and ${S}^1$–equivariant cobordism theory), Diplomarbeit, Bonn (1991) arXiv:math.AT/0405232
24 M J Hopkins, Topological modular forms, the Witten genus, and the theorem of the cube, from: "Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Zürich, 1994)", Birkhäuser (1995) 554 MR1403956
25 M J Hopkins, Algebraic topology and modular forms, from: "Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002)", Higher Ed. Press (2002) 291 MR1989190
26 N M Katz, $p$-adic properties of modular schemes and modular forms, from: "Modular functions of one variable, III (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972)", Springer (1973) MR0447119
27 J Kramer, An arithmetic theory of Jacobi forms in higher dimensions, J. Reine Angew. Math. 458 (1995) 157 MR1310957
28 I M Krichever, Generalized elliptic genera and Baker-Akhiezer functions, Mat. Zametki 47 (1990) 34, 158 MR1048541
29 L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, Lecture Notes in Math. 1213, Springer (1986) MR866482
30 J E McClure, $E_\infty$–ring structures for Tate spectra, Proc. Amer. Math. Soc. 124 (1996) 1917 MR1307549
31 I Rosu, Equivariant elliptic cohomology and rigidity, Amer. J. Math. 123 (2001) 647 MR1844573
32 Y B Rudyak, On Thom spectra, orientability, and cobordism, Springer Monographs in Mathematics, Springer (1998) MR1627486
33 R Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954) 17 MR0061823
34 E Witten, Elliptic genera and quantum field theory, Comm. Math. Phys. 109 (1987) 525 MR885560
35 E Witten, The index of the Dirac operator in loop space, from: "Elliptic curves and modular forms in algebraic topology (Princeton, NJ, 1986)", Lecture Notes in Math. 1326, Springer (1988) 161 MR970288