Volume 16, issue 4 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 6, 3133–3747
Issue 5, 2509–3131
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Rigidity in equivariant stable homotopy theory

Irakli Patchkoria

Algebraic & Geometric Topology 16 (2016) 2159–2227
Bibliography
1 J F Adams, On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960) 20
2 V Angeltveit, Topological Hochschild homology and cohomology of A ring spectra, Geom. Topol. 12 (2008) 987 MR2403804
3 D Barnes, C Roitzheim, Rational equivariant rigidity, from: "An alpine expedition through algebraic topology" (editors C Ausoni, K Hess, B Johnson, W Lück, J Scherer), Contemp. Math. 617, Amer. Math. Soc. (2014) 13 MR3243391
4 H J Baues, F Muro, Toda brackets and cup-one squares for ring spectra, Comm. Algebra 37 (2009) 56 MR2482810
5 A J Blumberg, Continuous functors as a model for the equivariant stable homotopy category, Algebr. Geom. Topol. 6 (2006) 2257 MR2286026
6 J M Boardman, On stable homotopy theory and some applications, PhD thesis, University of Cambridge (1964)
7 A K Bousfield, On the telescopic homotopy theory of spaces, Trans. Amer. Math. Soc. 353 (2001) 2391 MR1814075
8 A K Bousfield, E M Friedlander, Homotopy theory of Γ–spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory, II" (editors M G Barratt, M E Mahowald), Lecture Notes in Math. 658, Springer (1978) 80 MR513569
9 J M Cohen, The decomposition of stable homotopy, Ann. of Math. 87 (1968) 305
10 T tom Dieck, Transformation groups, 8, de Gruyter (1987)
11 D Dugger, B Shipley, K–theory and derived equivalences, Duke Math. J. 124 (2004) 587 MR2085176
12 D Dugger, B Shipley, A curious example of triangulated-equivalent model categories which are not Quillen equivalent, Algebr. Geom. Topol. 9 (2009) 135 MR2482071
13 W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
14 A D Elmendorf, Systems of fixed point sets, Trans. Amer. Math. Soc. 277 (1983) 275 MR690052
15 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
16 S I Gelfand, Y I Manin, Methods of homological algebra, Springer (2003) MR1950475
17 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
18 J P C Greenlees, J P May, Generalized Tate cohomology, 543, Amer. Math. Soc. (1995) MR1230773
19 B Guillou, J P May, Enriched model categories and presheaf categories, preprint (2013) arXiv:1110.3567
20 M Hausmann, G-symmetric spectra, semistability and the multiplicative norm, preprint (2014) arXiv:1411.2290
21 M A Hill, M J Hopkins, D C Ravenel, On the nonexistence of elements of Kervaire invariant one, Ann. of Math. (2) 184 (2016) 1 MR3505179
22 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
23 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
24 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
25 K Hutschenreuter, On rigidity of the ring spectra Pm§(p) and ko, PhD thesis, Universität Bonn (2012)
26 S Illman, The equivariant triangulation theorem for actions of compact Lie groups, Math. Ann. 262 (1983) 487 MR696520
27 D M Kan, Semisimplicial spectra, Illinois J. Math. 7 (1963) 463
28 G M Kelly, Basic concepts of enriched category theory, 64, Cambridge Univ. Press (1982) 245
29 L G Lewis Jr., The category of Mackey functors for a compact Lie group, from: "Group representations: cohomology, group actions and topology" (editors A Adem, J Carlson, S Priddy, P Webb), Proc. Sympos. Pure Math. 63, Amer. Math. Soc. (1998) 301 MR1603183
30 L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
31 M Lydakis, Simplicial functors and stable homotopy theory, unpublished manuscript (1998)
32 M A Mandell, Equivariant symmetric spectra, 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) 399 MR2066508
33 M A Mandell, J P May, Equivariant orthogonal spectra and S–modules, 755, Amer. Math. Soc. (2002) MR1922205
34 M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001) 441 MR1806878
35 J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
36 J P May, The Wirthmüller isomorphism revisited, Theory Appl. Categ. 11 (2003) 132 MR1988073
37 A Neeman, Triangulated categories, 148, Princeton Univ. Press (2001) MR1812507
38 I Patchkoria, On the algebraic classification of module spectra, Algebr. Geom. Topol. 12 (2012) 2329 MR3020210
39 D G Quillen, Homotopical algebra, 43, Springer (1967)
40 C Roitzheim, Rigidity and exotic models for the K–local stable homotopy category, Geom. Topol. 11 (2007) 1855 MR2350470
41 M Schlichting, A note on K–theory and triangulated categories, Invent. Math. 150 (2002) 111 MR1930883
42 S Schwede, The stable homotopy category has a unique model at the prime 2, Adv. Math. 164 (2001) 24 MR1870511
43 S Schwede, The stable homotopy category is rigid, Ann. of Math. 166 (2007) 837 MR2373374
44 S Schwede, Algebraic versus topological triangulated categories, from: "Triangulated categories" (editor Cambridge), London Math. Soc. Lecture Note Ser. 375, Cambridge Univ. Press (2010) 389 MR2681714
45 S Schwede, Lectures on equivariant stable homotopy theory, lecture notes (2014)
46 S Schwede, B Shipley, A uniqueness theorem for stable homotopy theory, Math. Z. 239 (2002) 803 MR1902062
47 S Schwede, B Shipley, Stable model categories are categories of modules, Topology 42 (2003) 103 MR1928647
48 M Stolz, Equivariant structures on smash powers of commutative ring spectra, PhD thesis, University of Bergen (2011)
49 H Toda, Composition methods in homotopy groups of spheres, 49, Princeton Univ. Press (1962)
50 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324