Algebraic & Geometric Topology Volume 22, issue 4 (2022)

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ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

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$\mathrm{tmf}$–based Mahowald invariants

J D Quigley

Algebraic & Geometric Topology 22 (2022) 1789–1839

DOI: 10.2140/agt.2022.22.1789

Bibliography

1	J F Adams, On the groups J(X), IV, Topology 5 (1966) 21 MR198470
2	S M Bailey, N Ricka, On the Tate spectrum of tmf at the prime 2, Math. Z. 291 (2019) 821 MR3936090
3	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. (2008) 11 MR2508200
4	M Behrens, Root invariants in the Adams spectral sequence, Trans. Amer. Math. Soc. 358 (2006) 4279 MR2231379
5	M Behrens, Some root invariants at the prime 2, from: "Proceedings of the Nishida Fest" (editors M Ando, N Minami, J Morava, W S Wilson), Geom. Topol. Monogr. 10, Geom. Topol. (2007) 1 MR2402775
6	M Behrens, M Hill, M J Hopkins, M Mahowald, On the existence of a v₂³²–self map on M(1,4) at the prime 2, Homology Homotopy Appl. 10 (2008) 45 MR2475617
7	P Bhattacharya, P Egger, A class of 2–local finite spectra which admit a v₂¹–self-map, Adv. Math. 360 (2020) MR4031119
8	R R Bruner, Ext in the nineties, from: "Algebraic topology" (editor M C Tangora), Contemp. Math. 146, Amer. Math. Soc. (1993) 71 MR1224908
9	R R Bruner, Some root invariants and Steenrod operations in Ext_A(F₂,F₂), from: "Homotopy theory via algebraic geometry and group representations" (editors M Mahowald, S Priddy), Contemp. Math. 220, Amer. Math. Soc. (1998) 27 MR1642887
10	R Bruner, J Greenlees, The Bredon–Löﬄer conjecture, Experiment. Math. 4 (1995) 289 MR1387694
11	R L Cohen, W H Lin, M E Mahowald, The Adams spectral sequence of the real projective spaces, Pacific J. Math. 134 (1988) 27 MR953499
12	D M Davis, M Mahowald, Ext over the subalgebra A₂ of the Steenrod algebra for stunted projective spaces, from: "Current trends in algebraic topology, I" (editors R M Kane, S O Kochman, P S Selick, V P Snaith), CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 297 MR686123
13	D M Davis, M Mahowald, The spectrum (P ∧ bo)_−∞, Math. Proc. Cambridge Philos. Soc. 96 (1984) 85 MR743704
14	D M Davis, M Mahowald, Classification of the stable homotopy types of stunted real projective spaces, Pacific J. Math. 125 (1986) 335 MR863530
15	J P C Greenlees, J P May, Generalized Tate cohomology, Amer. Math. Soc. (1995) MR1230773
16	A G Henriques, The homotopy groups of tmf and of its localizations, from: "Topological modular forms" (editors C L Douglas, J Francis, A G Henriques, M A Hill), Amer. Math. Soc. (2014) 189 MR3223024
17	M J Hopkins, J Lin, X D Shi, Z Xu, Intersection forms of spin 4–manifolds and the Pin(2)–equivariant Mahowald invariant, Comm. Amer. Math. Soc. 2 (2022) 22 MR4385297
18	D C Isaksen, Stable stems, 1269, Amer. Math. Soc. (2019) MR4046815
19	W H Lin, D M Davis, M E Mahowald, J F Adams, Calculation of Lin’s Ext groups, Math. Proc. Cambridge Philos. Soc. 87 (1980) 459 MR569195
20	M Mahowald, The metastable homotopy of Sⁿ, 72, Amer. Math. Soc. (1967) 81 MR0236923
21	M E Mahowald, D C Ravenel, Toward a global understanding of the homotopy groups of spheres, from: "The Lefschetz centennial conference, II" (editor S Gitler), Contemp. Math. 58, Amer. Math. Soc. (1987) 57 MR893848
22	M E Mahowald, D C Ravenel, The root invariant in homotopy theory, Topology 32 (1993) 865 MR1241877
23	M Mahowald, P Shick, Periodic phenomena in the classical Adams spectral sequence, Trans. Amer. Math. Soc. 300 (1987) 191 MR871672
24	H R Miller, D C Ravenel, W S Wilson, Periodic phenomena in the Adams–Novikov spectral sequence, Ann. of Math. 106 (1977) 469 MR458423
25	A Perry, resolution, computes some Ext relevant to algebraic topology (2013)
26	J D Quigley, The motivic Mahowald invariant, Algebr. Geom. Topol. 19 (2019) 2485 MR4023321
27	J D Quigley, Motivic Mahowald invariants over general base fields, Doc. Math. 26 (2021) 561 MR4282796
28	J D Quigley, Real motivic and C₂–equivariant Mahowald invariants, J. Topol. 14 (2021) 369 MR4235014
29	D C Ravenel, Complex cobordism and stable homotopy groups of spheres, 121, Academic (1986) MR860042
30	H Sadofsky, The root invariant and v₁–periodic families, Topology 31 (1992) 65 MR1153239
31	R Schultz, Exotic spheres as stationary sets of homotopy sphere involutions, Michigan Math. J. 29 (1982) 121 MR646378
32	P Shick, On root invariants of periodic classes in Ext_A(ℤ∕2, ℤ∕2), Trans. Amer. Math. Soc. 301 (1987) 227 MR879570
33	P Shick, On a conjecture of Mahowald on the cohomology of finite sub-Hopf algebras of the Steenrod algebra, Homology Homotopy Appl. 22 (2020) 59 MR4093169
34	N Shimada, A Iwai, On the cohomology of some Hopf algebras, Nagoya Math. J. 30 (1967) 103 MR215896
35	L Smith, On realizing complex bordism modules : applications to the stable homotopy of spheres, Amer. J. Math. 92 (1970) 793 MR275429
36	S Stolz, Involutions on spheres and Mahowald’s root invariant, Math. Ann. 281 (1988) 109 MR944605
37	H Toda, On spectra realizing exterior parts of the Steenrod algebra, Topology 10 (1971) 53 MR271933