Algebraic & Geometric Topology Volume 23, issue 9 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

Beta families arising from a $v_2^9$ self-map on $S/(3,v_1^8)$

Eva Belmont and Katsumi Shimomura

Algebraic & Geometric Topology 23 (2023) 4349–4378

DOI: 10.2140/agt.2023.23.4349

Bibliography

1	T Bauer, Computation of the homotopy of the spectrum tmf, from: "Groups, homotopy and configuration spaces" (editors N Iwase, T Kohno, R Levi, D Tamaki, J Wu), Geom. Topol. Monogr. 13, Geom. Topol. Publ. (2008) 11 MR2508200
2	M Behrens, M Mahowald, J D Quigley, The 2–primary Hurewicz image of tmf, Geom. Topol. 27 (2023) 2763 MR4645486
3	M Behrens, S Pemmaraju, On the existence of the self map v₂⁹ on the Smith–Toda complex V (1) at the prime 3, from: "Homotopy theory : relations with algebraic geometry, group cohomology, and algebraic K–theory" (editors P Goerss, S Priddy), Contemp. Math. 346, Amer. Math. Soc. (2004) 9 MR2066495
4	E Belmont, G Wang, Adams–Novikov data, online data set (2023)
5	E Belmont, G Wang, MinimalResolution (code for computing algebraic Novikov spectral sequence, p = 3 version), source code (2023)
6	P G Goerss, The Adams–Novikov spectral sequence and the homotopy groups of spheres, lecture notes (2008) arXiv:0802.1006
7	H W Henn, N Karamanov, M Mahowald, The homotopy of the K(2)–local Moore spectrum at the prime 3 revisited, Math. Z. 275 (2013) 953 MR3127044
8	A G Henriques, The homotopy groups of tmf and of its localizations (editors C L Douglas, J Francis, A G Henriques, M A Hill), 201, Amer. Math. Soc. (2014) 189 MR3223024
9	H R Miller, D C Ravenel, W S Wilson, Periodic phenomena in the Adams–Novikov spectral sequence, Ann. of Math. 106 (1977) 469 MR0458423
10	S Oka, Ring spectra with few cells, Japan. J. Math. 5 (1979) 81 MR0614695
11	S Oka, Note on the β–family in stable homotopy of spheres at the prime 3, Mem. Fac. Sci. Kyushu Univ. Ser. A 35 (1981) 367 MR0628729
12	J H Palmieri, Stable homotopy over the Steenrod algebra, 716, Amer. Math. Soc. (2001) MR1821838
13	D C Ravenel, The non-existence of odd primary Arf invariant elements in stable homotopy, Math. Proc. Cambridge Philos. Soc. 83 (1978) 429 MR0474291
14	D C Ravenel, Complex cobordism and stable homotopy groups of spheres, 121, Academic (1986) MR0860042
15	K Shimomura, The homotopy groups of the L₂–localized Toda–Smith spectrum V (1) at the prime 3, Trans. Amer. Math. Soc. 349 (1997) 1821 MR1370651
16	K Shimomura, The existence of β_9t+3 in the stable homotopy of spheres at the prime three, preprint (2006)
17	K Shimomura, The beta elements β_tp²∕r in the homotopy of spheres, Algebr. Geom. Topol. 10 (2010) 2079 MR2745666
18	K Shimomura, Note on beta elements in homotopy, and an application to the prime three case, Proc. Amer. Math. Soc. 138 (2010) 1495 MR2578544
19	H Toda, On spectra realizing exterior parts of the Steenrod algebra, Topology 10 (1971) 53 MR0271933
20	G Wang, Computations of the Adams–Novikov E₂–term, Chinese Ann. Math. Ser. B 42 (2021) 551 MR4289191
21	G Wang, MinimalResolution (code for computing algebraic Novikov spectral sequence), source code (2023)