Geodesic
The beta family at the prime two and modular forms of level three
von Bodecker, Hanno1
1Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2851-2864
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We use the orientation underlying the Hirzebruch genus of level three to map the beta family at the prime p = 2 into the ring of divided congruences. This procedure, which may be thought of as the elliptic Greek letter beta construction, yields the f–invariants of this family.

DOI : 10.2140/agt.2016.16.2851
Classification : 55Q45, 11F11, 55Q51, 58J26
Keywords: stable homotopy of spheres, Greek letter construction, elliptic genera

von Bodecker, Hanno  1

1 Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany 
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von Bodecker, Hanno. The beta family at the prime two and modular forms of level three. Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 2851-2864. doi: 10.2140/agt.2016.16.2851

[1] M Behrens, Congruences between modular forms given by the divided β family in homotopy theory, Geom. Topol. 13 (2009) 319 | DOI

[2] M Behrens, G Laures, β–family congruences and the f–invariant, from: "New topological contexts for Galois theory and algebraic geometry" (editors A Baker, B Richter), Geom. Topol. Monogr. 16 (2009) 9 | DOI

[3] H Von Bodecker, On the geometry of the f–invariant, PhD thesis (2008)

[4] H Von Bodecker, On the f–invariant of products, Homology Homotopy Appl. 18 (2016) 169 | DOI

[5] U Bunke, N Naumann, The f–invariant and index theory, Manuscripta Math. 132 (2010) 365 | DOI

[6] J Franke, On the construction of elliptic cohomology, Math. Nachr. 158 (1992) 43 | DOI

[7] F Hirzebruch, T Berger, R Jung, Manifolds and modular forms, E20, Friedr. Vieweg Sohn (1992) | DOI

[8] J Hornbostel, N Naumann, Beta-elements and divided congruences, Amer. J. Math. 129 (2007) 1377 | DOI

[9] G Laures, The topological q–expansion principle, Topology 38 (1999) 387 | DOI

[10] H R Miller, D C Ravenel, W S Wilson, Periodic phenomena in the Adams–Novikov spectral sequence, Ann. of Math. 106 (1977) 469 | DOI

[11] D C Ravenel, Complex cobordism and stable homotopy groups of spheres, 347, Amer. Math. Soc. (2003)

[12] K Shimomura, Novikov’s Ext2 at the prime 2, Hiroshima Math. J. 11 (1981) 499

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