Volume 11, issue 4 (2011)

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ISSN (electronic): 1472-2739
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Toda brackets and congruences of modular forms

Gerd Laures

Algebraic & Geometric Topology 11 (2011) 1893–1914
Bibliography
1 J F Adams, On the groups $J(X)$ IV, Topology 5 (1966) 21 MR0198470
2 A Baker, Elliptic genera of level $N$ and elliptic cohomology, J. London Math. Soc. $(2)$ 49 (1994) 581 MR1271552
3 A Baker, Operations and cooperations in elliptic cohomology I: Generalized modular forms and the cooperation algebra, New York J. Math. 1 (1994/95) 39 MR1307488
4 A Baker, Hecke operations and the Adams $E_2$–term based on elliptic cohomology, Canad. Math. Bull. 42 (1999) 129 MR1692001
5 M G Barratt, J D S Jones, M E Mahowald, Relations amongst Toda brackets and the Kervaire invariant in dimension 62, J. London Math. Soc. $(2)$ 30 (1984) 533 MR810962
6 M Behrens, Congruences between modular forms given by the divided $\beta$ family in homotopy theory, Geom. Topol. 13 (2009) 319 MR2469520
7 M Behrens, G Laures, $\beta$–family congruences and the $f$–invariant, from: "New topological contexts for Galois theory and algebraic geometry (BIRS 2008)", Geom. Topol. Monogr. 16, Geom. Topol. Publ., Coventry (2009) 9 MR2544384
8 H von Bodecker, The beta family at the prime two and modular forms of level three arXiv:0912.3082
9 H von Bodecker, On the $f$–invariant of products arXiv:0808.0428
10 H von Bodecker, On the geometry of hte $f$ invariant arXiv:0909.3968
11 J L Brylinski, Representations of loop groups, Dirac operators on loop space, and modular forms, Topology 29 (1990) 461 MR1071369
12 U Bunke, N Naumann, The $f$–invariant and index theory, Manuscripta Math. 132 (2010) 365 MR2652438
13 U Bunke, N Naumann, The $f$–invariant and index theory, Manuscripta Math. 132 (2010) 365 MR2652438
14 J Franke, On the construction of elliptic cohomology, Math. Nachr. 158 (1992) 43 MR1235295
15 J Hornbostel, N Naumann, Beta-elements and divided congruences, Amer. J. Math. 129 (2007) 1377 MR2354323
16 N M Katz, Higher congruences between modular forms, Ann. of Math. $(2)$ 101 (1975) 332 MR0417059
17 S O Kochman, Stable homotopy groups of spheres, Lecture Notes in Mathematics 1423, Springer (1990) MR1052407
18 S O Kochman, Bordism, stable homotopy and Adams spectral sequences, Fields Institute Monographs 7, American Mathematical Society (1996) MR1407034
19 G Laures, The topological $q$–expansion principle, Topology 38 (1999) 387 MR1660325
20 G Laures, On cobordism of manifolds with corners, Trans. Amer. Math. Soc. 352 (2000) 5667 MR1781277
21 G Laures, $K(1)$–local topological modular forms, Invent. Math. 157 (2004) 371 MR2076927
22 T Lawson, N Naumann, Topological modular forms of level 3 and $E_{\infty}$–structures on truncated Brown–Peterson spectra arXiv:1101.3897
23 J P May, Matric Massey products, J. Algebra 12 (1969) 533 MR0238929
24 H R Miller, D C Ravenel, W S Wilson, Periodic phenomena in the Adams–Novikov spectral sequence, Ann. Math. $(2)$ 106 (1977) 469 MR0458423
25 D C Ravenel, Complex cobordism and stable homotopy groups of spheres, Pure and Applied Mathematics 121, Academic Press (1986) MR860042
26 J P Serre, Formes modulaires et fonctions zêta $p$–adiques, from: "Modular functions of one variable, III (Proc Internat. Summer School, Univ. Antwerp, 1972)", Springer (1973) MR0404145
27 K Shimomura, Novikov's $\mathrm{Ext}^{2}$ at the prime 2, Hiroshima Math. J. 11 (1981) 499 MR635034