Volume 5, issue 3 (2005)

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

Volume 19
Issue 6, 2677–3215
Issue 5, 2151–2676
Issue 4, 1619–2150
Issue 3, 1079–1618
Issue 2, 533–1078
Issue 1, 1–532

Volume 18, 7 issues

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

Author Index
The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
To Appear
 
Other MSP Journals
Hopf algebra structure on topological Hochschild homology

Vigleik Angeltveit and John Rognes

Algebraic & Geometric Topology 5 (2005) 1223–1290
Bibliography
1 J F Adams, S B Priddy, Uniqueness of $B\mathrm{SO}$, Math. Proc. Cambridge Philos. Soc. 80 (1976) 475 MR0431152
2 V Angeltveit, Hopf algebra structure on topological Hochschild homology (2002)
3 S Araki, H Toda, Multiplicative structures in $\mathrm{mod} q$ cohomology theories I, Osaka J. Math. 2 (1965) 71 MR0182967
4 C Ausoni, Topological Hochschild homology of connective complex $K$–theory, Amer. J. Math. 127 (2005) 1261 MR2183525
5 C Ausoni, J Rognes, Algebraic $K$–theory of topological $K$–theory, Acta Math. 188 (2002) 1 MR1947457
6 N A Baas, I Madsen, On the realization of certain modules over the Steenrod algebra, Math. Scand. 31 (1972) 220 MR0377879
7 A Baker, A Jeanneret, Brave new Hopf algebroids and extensions of $M$U-algebras, Homology Homotopy Appl. 4 (2002) 163 MR1937961
8 A Baker, B Richter, On the $\Gamma$–cohomology of rings of numerical polynomials and $E_\infty$ structures on $K$–theory, Comment. Math. Helv. 80 (2005) 691 MR2182697
9 M Bökstedt, Topological Hochschild homology, preprint, University of Bielefeld (c.1986)
10 M Bökstedt, The topological Hochschild homology of $\mathbb{Z}$ and $\mathbb{Z}/p$, preprint, University of Bielefeld (c.1986)
11 M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic $K$–theory of spaces, Invent. Math. 111 (1993) 465 MR1202133
12 M Bökstedt, I Madsen, Topological cyclic homology of the integers, Astérisque (1994) 7, 57 MR1317117
13 R R Bruner, J P May, J E McClure, M Steinberger, $H_\infty $ ring spectra and their applications, Lecture Notes in Mathematics 1176, Springer (1986) MR836132
14 R R Bruner, J Rognes, Differentials in the homological homotopy fixed point spectral sequence, Algebr. Geom. Topol. 5 (2005) 653 MR2153113
15 H Cartan, S Eilenberg, Homological algebra, Princeton University Press (1956) MR0077480
16 D M Davis, The cohomology of the spectrum $bJ$, Bol. Soc. Mat. Mexicana $(2)$ 20 (1975) 6 MR0467749
17 B I Dundas, Relative $K$–theory and topological cyclic homology, Acta Math. 179 (1997) 223 MR1607556
18 D M Davis, M Mahowald, $v_{1}$– and $v_{2}$–periodicity in stable homotopy theory, Amer. J. Math. 103 (1981) 615 MR623131
19 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Mathematical Surveys and Monographs 47, American Mathematical Society (1997) MR1417719
20 Z Fiedorowicz, R M Vogt, Topological Hochschild homology of $E_n$ ring spectra arXiv:math.AT/0410367
21 L Hesselholt, I Madsen, On the $K$–theory of finite algebras over Witt vectors of perfect fields, Topology 36 (1997) 29 MR1410465
22 L Hesselholt, I Madsen, On the $K$–theory of local fields, Ann. of Math. $(2)$ 158 (2003) 1 MR1998478
23 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
24 T J Hunter, On the homology spectral sequence for topological Hochschild homology, Trans. Amer. Math. Soc. 348 (1996) 3941 MR1376548
25 D C Johnson, W S Wilson, Projective dimension and Brown–Peterson homology, Topology 12 (1973) 327 MR0334257
26 A Lazarev, Towers of $M$U-algebras and the generalized Hopkins–Miller theorem, Proc. London Math. Soc. $(3)$ 87 (2003) 498 MR1990937
27 L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, Lecture Notes in Mathematics 1213, Springer (1986) MR866482
28 S Lunøe-Nielsen, A homological approach to topological cyclic theory (2005)
29 S Mac Lane, Homology, Classics in Mathematics, Springer (1995) MR1344215
30 M Mahowald, R J Milgram, Operations which detect Sq4 in connective $K$–theory and their applications, Quart. J. Math. Oxford Ser. $(2)$ 27 (1976) 415 MR0433453
31 M Mahowald, The image of $J$ in the $EHP$ sequence, Ann. of Math. $(2)$ 116 (1982) 65 MR662118
32 J P May, $E_{\infty }$ ring spaces and $E_{\infty }$ ring spectra, Lecture Notes in Mathematics 577, Springer (1977) 268 MR0494077
33 R McCarthy, Relative algebraic $K$–theory and topological cyclic homology, Acta Math. 179 (1997) 197 MR1607555
34 J McClure, R Schwänzl, R Vogt, $THH(R)\cong R\otimes S^1$ for $E_\infty$ ring spectra, J. Pure Appl. Algebra 121 (1997) 137 MR1473888
35 J E McClure, R E Staffeldt, On the topological Hochschild homology of $b\mathrm{u}$ I, Amer. J. Math. 115 (1993) 1 MR1209233
36 J Milnor, The Steenrod algebra and its dual, Ann. of Math. $(2)$ 67 (1958) 150 MR0099653
37 J W Milnor, J C Moore, On the structure of Hopf algebras, Ann. of Math. $(2)$ 81 (1965) 211 MR0174052
38 S Oka, Ring spectra with few cells, Japan. J. Math. $($N.S.$)$ 5 (1979) 81 MR614695
39 D C Ravenel, Complex cobordism and stable homotopy groups of spheres, Pure and Applied Mathematics 121, Academic Press (1986) MR860042
40 C Rezk, Supplementary notes for Math 512 (2001)
41 A Robinson, Obstruction theory and the strict associativity of Morava $K$–theories, from: "Advances in homotopy theory (Cortona, 1988)", London Math. Soc. Lecture Note Ser. 139, Cambridge Univ. Press (1989) 143 MR1055874
42 J Rognes, The smooth Whitehead spectrum of a point at odd regular primes, Geom. Topol. 7 (2003) 155 MR1988283
43 J D Stasheff, Homotopy associativity of $H$–spaces I, II, Trans. Amer. Math. Soc. 108 $(1963)$, 275-292; ibid. 108 (1963) 293 MR0158400
44 J Stasheff, From operads to “physically” inspired theories, from: "Operads: Proceedings of Renaissance Conferences (Hartford, CT/Luminy, 1995)", Contemp. Math. 202, Amer. Math. Soc. (1997) 53 MR1436917
45 R E Stong, Determination of $H^*(\mathrm{BO}(k,\ldots,\infty),\mathbb{Z}_{2})$ and $H^*(\mathrm{BU}(k,\ldots,\infty),\mathbb{Z}_{2})$, Trans. Amer. Math. Soc. 107 (1963) 526 MR0151963
46 N P Strickland, Products on $\mathrm{MU}$–modules, Trans. Amer. Math. Soc. 351 (1999) 2569 MR1641115
47 W S Wilson, The $\Omega $–spectrum for Brown–Peterson cohomology. II, Amer. J. Math. 97 (1975) 101 MR0383390
48 R Zahler, The Adams–Novikov spectral sequence for the spheres, Ann. of Math. $(2)$ 96 (1972) 480 MR0319197