Algebraic & Geometric Topology Volume 17, issue 5 (2017)

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 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Higher Toda brackets and the Adams spectral sequence in triangulated categories

J Daniel Christensen and Martin Frankland

Algebraic & Geometric Topology 17 (2017) 2687–2735

DOI: 10.2140/agt.2017.17.2687

Bibliography

1	J F Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960) 20 MR0141119
2	J F Adams, Stable homotopy and generalised homology, Univ. of Chicago Press (1974) MR0402720
3	P Balmer, Triangulated categories with several triangulations, (2002)
4	T Barthel, J P May, E Riehl, Six model structures for DG-modules over DGAs : model category theory in homological action, New York J. Math. 20 (2014) 1077 MR3291613
5	H J Baues, D Blanc, Higher order derived functors and the Adams spectral sequence, J. Pure Appl. Algebra 219 (2015) 199 MR3250522
6	H J Baues, M Jibladze, Secondary derived functors and the Adams spectral sequence, Topology 45 (2006) 295 MR2193337
7	H J Baues, M Jibladze, Dualization of the Hopf algebra of secondary cohomology operations and the Adams spectral sequence, J. K-Theory 7 (2011) 203 MR2787297
8	D Benson, H Krause, S Schwede, Realizability of modules over Tate cohomology, Trans. Amer. Math. Soc. 356 (2004) 3621 MR2055748
9	N Bourbaki, Commutative algebra, Chapters 1–7, Hermann (1972) MR0360549
10	R R Bruner, An Adams spectral sequence primer, (2009)
11	J F Carlson, Modules and group algebras, Birkhäuser (1996) MR1393196
12	S K Chebolu, J D Christensen, J Mináč, Ghosts in modular representation theory, Adv. Math. 217 (2008) 2782 MR2397466
13	J D Christensen
14	J D Christensen, Ideals in triangulated categories: phantoms, ghosts and skeleta, Adv. Math. 136 (1998) 284 MR1626856
15	J M Cohen, The decomposition of stable homotopy, Ann. of Math. 87 (1968) 305 MR0231377
16	S Eilenberg, J C Moore, Homology and fibrations, I : Coalgebras, cotensor product and its derived functors, Comment. Math. Helv. 40 (1966) 199 MR0203730
17	A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, 47, Amer. Math. Soc. (1997) MR1417719
18	S I Gelfand, Y I Manin, Methods of homological algebra, Springer (2003) MR1950475
19	J R Harper, Secondary cohomology operations, 49, Amer. Math. Soc. (2002) MR1913285
20	A Heller, Stable homotopy categories, Bull. Amer. Math. Soc. 74 (1968) 28 MR0224090
21	M Hovey, J H Palmieri, N P Strickland, Axiomatic stable homotopy theory, 610, Amer. Math. Soc. (1997) MR1388895
22	M Hovey, N P Strickland, Morava K–theories and localisation, 666, Amer. Math. Soc. (1999) MR1601906
23	S Klaus, Towers and pyramids, I, Forum Math. 13 (2001) 663 MR1858494
24	S O Kochman, Uniqueness of Massey products on the stable homotopy of spheres, Canad. J. Math. 32 (1980) 576 MR586976
25	I Kříž, J P May, Operads, algebras, modules and motives, 233, Soc. Math. France (1995) MR1361938
26	H R Margolis, Spectra and the Steenrod algebra, 29, North-Holland (1983) MR738973
27	A Mathew, Second homotopy group of the mod 2 Moore spectrum
28	C R F Mauder, On the differentials in the Adams spectral sequence, Proc. Cambridge Philos. Soc. 60 (1964) 409 MR0167980
29	C R F Maunder, Cohomology operations of the N^th kind, Proc. London Math. Soc. 13 (1963) 125 MR0211398
30	J C McKeown, Toda bracket, (2012)
31	L Meier, United elliptic homology, PhD thesis, Universität Bonn (2012)
32	R E Mosher, M C Tangora, Cohomology operations and applications in homotopy theory, Harper & Row (1968) MR0226634
33	A Neeman, Triangulated categories, 148, Princeton Univ. Press (2001) MR1812507
34	I Patchkoria, On the algebraic classification of module spectra, Algebr. Geom. Topol. 12 (2012) 2329 MR3020210
35	D C Ravenel, Complex cobordism and stable homotopy groups of spheres, 121, Academic Press (1986) MR860042
36	S Sagave, Universal Toda brackets of ring spectra, Trans. Amer. Math. Soc. 360 (2008) 2767 MR2373333
37	S Schwede, Algebraic versus topological triangulated categories, from: "Triangulated categories" (editors T Holm, P Jørgensen, R Rouquier), London Math. Soc. Lecture Note Ser. 375, Cambridge Univ. Press (2010) 389 MR2681714
38	S Schwede, Symmetric spectra, preprint (2012)
39	S Schwede, B Shipley, Stable model categories are categories of modules, Topology 42 (2003) 103 MR1928647
40	B Shipley, An algebraic model for rational S¹–equivariant stable homotopy theory, Q. J. Math. 53 (2002) 87 MR1887672
41	B Shipley, Hℤ–algebra spectra are differential graded algebras, Amer. J. Math. 129 (2007) 351 MR2306038
42	E Spanier, Higher order operations, Trans. Amer. Math. Soc. 109 (1963) 509 MR0158399
43	H Toda, Composition methods in homotopy groups of spheres, 49, Princeton Univ. Press (1962) MR0143217
44	C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324