Volume 23, issue 2 (2019)

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

Volume 24, 1 issue

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Derived induction and restriction theory

Akhil Mathew, Niko Naumann and Justin Noel

Geometry & Topology 23 (2019) 541–636
Bibliography
1 J F Adams, Prerequisites (on equivariant stable homotopy) for Carlsson’s lecture, from: "Algebraic topology, Aarhus 1982" (editors I Madsen, B Oliver), Lecture Notes in Math. 1051, Springer (1984) 483 MR764596
2 A Adem, R J Milgram, Cohomology of finite groups, 309, Springer (2004) MR2035696
3 D W Anderson, E H Brown Jr., F P Peterson, The structure of the Spin cobordism ring, Ann. of Math. 86 (1967) 271 MR0219077
4 M Ando, M Hopkins, C Rezk, Multiplicative orientations of KO–theory and of the spectrum of topological modular forms, preprint (2006)
5 V Angeltveit, Topological Hochschild homology and cohomology of A ring spectra, Geom. Topol. 12 (2008) 987 MR2403804
6 M F Atiyah, Characters and cohomology of finite groups, Inst. Hautes Études Sci. Publ. Math. 9 (1961) 23 MR0148722
7 M F Atiyah, K–theory and reality, Quart. J. Math. Oxford Ser. 17 (1966) 367 MR0206940
8 M F Atiyah, Bott periodicity and the index of elliptic operators, Quart. J. Math. Oxford Ser. 19 (1968) 113 MR0228000
9 M F Atiyah, I G Macdonald, Introduction to commutative algebra, Addison-Wesley (1969) MR0242802
10 M F Atiyah, G B Segal, Equivariant K–theory and completion, J. Differential Geometry 3 (1969) 1 MR0259946
11 P Balmer, Descent in triangulated categories, Math. Ann. 353 (2012) 109 MR2910783
12 P Balmer, Separable extensions in tensor-triangular geometry and generalized Quillen stratification, Ann. Sci. Éc. Norm. Supér. 49 (2016) 907 MR3552016
13 P Balmer, I Dell’Ambrogio, B Sanders, Restriction to finite-index subgroups as étale extensions in topology, KK–theory and geometry, Algebr. Geom. Topol. 15 (2015) 3025 MR3426702
14 D Barnes, Splitting monoidal stable model categories, J. Pure Appl. Algebra 213 (2009) 846 MR2494375
15 C Barwick, Spectral Mackey functors and equivariant algebraic K–theory, I, Adv. Math. 304 (2017) 646 MR3558219
16 C Barwick, S Glasman, J Shah, Spectral Mackey functors and equivariant algebraic K–theory, II, preprint (2015) arXiv:1505.03098
17 M Behrens, The construction of tmf, from: "Topological modular forms" (editors C L Douglas, J Francis, A G Henriques, M A Hill), Mathematical Surveys and Monographs 201, Amer. Math. Soc. (2014) 131 MR3223024
18 J M Boardman, Conditionally convergent spectral sequences, from: "Homotopy invariant algebraic structures" (editors J P Meyer, J Morava, W S Wilson), Contemp. Math. 239, Amer. Math. Soc. (1999) 49 MR1718076
19 A Bojanowska, S Jackowski, A spectral sequence convergent to equivariant K–theory, from: "Topology symposium, Siegen 1979" (editors U Koschorke, W D Neumann), Lecture Notes in Math. 788, Springer (1980) 245 MR585662
20 A K Bousfield, Homotopy spectral sequences and obstructions, Israel J. Math. 66 (1989) 54 MR1017155
21 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
22 G E Bredon, Equivariant cohomology theories, 34, Springer (1967) MR0214062
23 T Bröcker, E C Hook, Stable equivariant bordism, Math. Z. 129 (1972) 269 MR0321119
24 J F Carlson, Cohomology and induction from elementary abelian subgroups, Q. J. Math. 51 (2000) 169 MR1765788
25 G Carlsson, Equivariant stable homotopy and Segal’s Burnside ring conjecture, Ann. of Math. 120 (1984) 189 MR763905
26 H Cartan, S Eilenberg, Homological algebra, Princeton Univ. Press (1956) MR0077480
27 S R Costenoble, An introduction to equivariant cobordism MR1413302
28 T tom Dieck, Bordism of G–manifolds and integrality theorems, Topology 9 (1970) 345 MR0266241
29 T tom Dieck, Transformation groups, 8, de Gruyter (1987) MR889050
30 A W M Dress, Contributions to the theory of induced representations, from: "Algebraic K–theory, II : ‘Classical’ algebraic K–theory and connections with arithmetic" (editor H Bass), Lecture Notes in Math. 342, Springer (1973) 183 MR0384917
31 A W M Dress, Induction and structure theorems for orthogonal representations of finite groups, Ann. of Math. 102 (1975) 291 MR0387392
32 D. Dugger, A primer on homotopy colimits, book project (2008)
33 W G Dwyer, Homology decompositions for classifying spaces of finite groups, Topology 36 (1997) 783 MR1432421
34 W G Dwyer, Sharp homology decompositions for classifying spaces of finite groups, 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) 197 MR1603159
35 W G Dwyer, J P C Greenlees, Complete modules and torsion modules, Amer. J. Math. 124 (2002) 199 MR1879003
36 L Fajstrup, Tate cohomology of periodic K–theory with reality is trivial, Trans. Amer. Math. Soc. 347 (1995) 1841 MR1273490
37 H Fausk, Generalized Artin and Brauer induction for compact Lie groups, Trans. Amer. Math. Soc. 360 (2008) 5043 MR2403712
38 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
39 J A Green, Axiomatic representation theory for finite groups, J. Pure Appl. Algebra 1 (1971) 41 MR0279208
40 J P C Greenlees, Homotopy equivariance, strict equivariance and induction theory, Proc. Edinburgh Math. Soc. 35 (1992) 473 MR1187009
41 J P C Greenlees, Equivariant connective K–theory for compact Lie groups, J. Pure Appl. Algebra 187 (2004) 129 MR2027899
42 J P C Greenlees, Equivariant versions of real and complex connective K–theory, Homology Homotopy Appl. 7 (2005) 63 MR2205170
43 J P C Greenlees, J P May, Completions in algebra and topology, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 255 MR1361892
44 J P C Greenlees, J P May, Generalized Tate cohomology, 543, Amer. Math. Soc. (1995) MR1230773
45 J P C Greenlees, J P May, Localization and completion theorems for MU–module spectra, Ann. of Math. 146 (1997) 509 MR1491447
46 J P C Greenlees, H Sadofsky, The Tate spectrum of vn–periodic complex oriented theories, Math. Z. 222 (1996) 391 MR1400199
47 J P C Greenlees, N P Strickland, Varieties and local cohomology for chromatic group cohomology rings, Topology 38 (1999) 1093 MR1688422
48 J Grodal, Higher limits via subgroup complexes, Ann. of Math. 155 (2002) 405 MR1906592
49 J Grodal, S D Smith, Propagating sharp group homology decompositions, Adv. Math. 200 (2006) 525 MR2200855
50 B Guillou, J P May, Models of G–spectra as presheaves of spectra, preprint (2011) arXiv:1110.3571
51 M A Hill, M J Hopkins, D C Ravenel, The Arf–Kervaire problem in algebraic topology : sketch of the proof, from: "Current developments in mathematics, 2010" (editors D Jerison, B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), Int. (2011) 1 MR2906370
52 M A Hill, M J Hopkins, D C Ravenel, On the nonexistence of elements of Kervaire invariant one, Ann. of Math. 184 (2016) 1 MR3505179
53 M J Hopkins, Global methods in homotopy theory, from: "Homotopy theory" (editors E Rees, J D S Jones), London Math. Soc. Lecture Note Ser. 117, Cambridge Univ. Press (1987) 73 MR932260
54 M J Hopkins, N J Kuhn, D C Ravenel, Generalized group characters and complex oriented cohomology theories, J. Amer. Math. Soc. 13 (2000) 553 MR1758754
55 M J Hopkins, J H Smith, Nilpotence and stable homotopy theory, II, Ann. of Math. 148 (1998) 1 MR1652975
56 M A Hovey, D C Ravenel, The 7–connected cobordism ring at p = 3, Trans. Amer. Math. Soc. 347 (1995) 3473 MR1297530
57 D Husemoller, Fibre bundles, 20, Springer (1994) MR1249482
58 D Husemöller, M Joachim, B Jurčo, M Schottenloher, Basic bundle theory and K–cohomology invariants, 726, Springer (2008) MR2377868
59 S Illman, The equivariant triangulation theorem for actions of compact Lie groups, Math. Ann. 262 (1983) 487 MR696520
60 S Jackowski, J McClure, Homotopy decomposition of classifying spaces via elementary abelian subgroups, Topology 31 (1992) 113 MR1153240
61 N J Kuhn, Tate cohomology and periodic localization of polynomial functors, Invent. Math. 157 (2004) 345 MR2076926
62 P S Landweber, Conjugations on complex manifolds and equivariant homotopy of MU, Bull. Amer. Math. Soc. 74 (1968) 271 MR0222890
63 L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, 1213, Springer (1986) MR866482
64 W Lück, Survey on classifying spaces for families of subgroups, from: "Infinite groups: geometric, combinatorial and dynamical aspects" (editors L Bartholdi, T Ceccherini-Silberstein, T Smirnova-Nagnibeda, A Zuk), Progr. Math. 248, Birkhäuser (2005) 269 MR2195456
65 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
66 J Lurie, Derived algebraic geometry, XII : Proper morphisms, completions, and the Grothendieck existence theorem, preprint (2011)
67 J. Lurie, Higher algebra, book project (2014)
68 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
69 M A Mandell, The smash product for derived categories in stable homotopy theory, Adv. Math. 230 (2012) 1531 MR2927347
70 M A Mandell, J P May, Equivariant orthogonal spectra and S–modules, 755, Amer. Math. Soc. (2002) MR1922205
71 A Mathew, A thick subcategory theorem for modules over certain ring spectra, Geom. Topol. 19 (2015) 2359 MR3375530
72 A Mathew, The homology of tmf, Homology Homotopy Appl. 18 (2016) 1 MR3515195
73 A Mathew, N Naumann, J Noel, Nilpotence and descent in equivariant stable homotopy theory, Adv. Math. 305 (2017) 994 MR3570153
74 A Mathew, V Stojanoska, The Picard group of topological modular forms via descent theory, Geom. Topol. 20 (2016) 3133 MR3590352
75 J P May, Equivariant homotopy and cohomology theory, 91, Amer. Math. Soc. (1996) MR1413302
76 J P May, J E McClure, A reduction of the Segal conjecture, from: "Current trends in algebraic topology, II" (editors R M Kane, S O Kochman, P S Selick, V P Snaith), CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 209 MR686147
77 D Nardin, Parametrized higher category theory and higher algebra, Exposé IV : Stability with respect to an orbital –category, preprint (2016) arXiv:1608.07704
78 D Quillen, The spectrum of an equivariant cohomology ring, I, Ann. of Math. 94 (1971) 549 MR0298694
79 D Quillen, The spectrum of an equivariant cohomology ring, II, Ann. of Math. 94 (1971) 573 MR0298694
80 D C Ravenel, Nilpotence and periodicity in stable homotopy theory, 128, Princeton Univ. Press (1992) MR1192553
81 Y B Rudyak, On Thom spectra, orientability, and cobordism, Springer (1998) MR1627486
82 G Segal, The representation ring of a compact Lie group, Inst. Hautes Études Sci. Publ. Math. 34 (1968) 113 MR0248277
83 J P Serre, Linear representations of finite groups, 42, Springer (1977) MR0450380
84 J H Silverman, The arithmetic of elliptic curves, 106, Springer (1986) MR817210
85 J Smith, Finite complexes with vanishing lines of small slope, preprint (2005)
86 R E Stong, Notes on cobordism theory, Princeton Univ. Press (1968) MR0248858
87 C T C Wall, Determination of the cobordism ring, Ann. of Math. 72 (1960) 292 MR0120654
88 S Waner, Mackey functors and G–cohomology, Proc. Amer. Math. Soc. 90 (1984) 641 MR733419
89 P Webb, A guide to Mackey functors, from: "Handbook of algebra, II" (editor M Hazewinkel), North-Holland (2000) 805 MR1759612