Volume 14, issue 2 (2010)

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

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

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
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Topological Hochschild homology of Thom spectra and the free loop space

Andrew J Blumberg, Ralph L Cohen and Christian Schlichtkrull

Geometry & Topology 14 (2010) 1165–1242
Bibliography
1 M Ando, A J Blumberg, D Gepner, M J Hopkins, C Rezk, Units of ring spectra and Thom spectra arXiv:0810.4535v3
2 A Baker, B Richter, Quasisymmetric functions from a topological point of view, Math. Scand. 103 (2008) 208 MR2484353
3 M Basterra, André–Quillen cohomology of commutative $S$–algebras, J. Pure Appl. Algebra 144 (1999) 111 MR1732625
4 M Basterra, M A Mandell, Homology and cohomology of $E_\infty$ ring spectra, Math. Z. 249 (2005) 903 MR2126222
5 A J Blumberg, Topological Hochschild homology of Thom spectra which are ${E}_\infty$ ring spectra arXiv:0811.0803
6 A J Blumberg, Progress towards the calculation of the $K$–theory of Thom spectra, PhD thesis, University of Chicago (2005)
7 J M Boardman, R M Vogt, Homotopy-everything $H$–spaces, Bull. Amer. Math. Soc. 74 (1968) 1117 MR0236922
8 M Bökstedt, The topological Hochschild homology of $\mathbb{Z}$ and $\mathbb{Z}/p$, Preprint (1985)
9 A K Bousfield, E M Friedlander, Homotopy theory of $\Gamma $–spaces, spectra, and bisimplicial sets, from: "Geometric applications of homotopy theory (Proc. Conf., Evanston, Ill., 1977), II", Lecture Notes in Math. 658, Springer (1978) 80 MR513569
10 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, Lecture Notes in Math. 304, Springer (1972) MR0365573
11 M Brun, Z Fiedorowicz, R M Vogt, On the multiplicative structure of topological Hochschild homology, Algebr. Geom. Topol. 7 (2007) 1633 MR2366174
12 S Bullett, Permutations and braids in cobordism theory, Proc. London Math. Soc. $(3)$ 38 (1979) 517 MR532985
13 F R Cohen, Braid orientations and bundles with flat connections, Invent. Math. 46 (1978) 99 MR493954
14 F R Cohen, J P May, L R Taylor, $K(\mathbb{Z}, 0)$ and $K(\mathbb{Z}_2, 0)$ as Thom spectra, Illinois J. Math. 25 (1981) 99 MR602900
15 W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
16 A D Elmendorf, I Kriz, M A Mandell, J P May, Rings, modules, and algebras in stable homotopy theory, Math. Surveys and Monogr. 47, Amer. Math. Soc. (1997) MR1417719
17 A D Elmendorf, I Kriz, M A Mandell, J P May, Errata for “Rings, modules, and algebras in stable homotopy theory” (2007)
18 T G Goodwillie, Cyclic homology, derivations, and the free loopspace, Topology 24 (1985) 187 MR793184
19 P S Hirschhorn, Model categories and their localizations, Math. Surveys and Monogr. 99, Amer. Math. Soc. (2003) MR1944041
20 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
21 N Iwase, A continuous localization and completion, Trans. Amer. Math. Soc. 320 (1990) 77 MR1031978
22 I Kriz, J P May, Operads, algebras, modules and motives, Astérisque 233 (1995) MR1361938
23 L G Lewis Jr., J P May, M Steinberger, J E McClure, Equivariant stable homotopy theory, Lecture Notes in Math. 1213, Springer (1986) MR866482
24 J Lillig, A union theorem for cofibrations, Arch. Math. $($Basel$)$ 24 (1973) 410 MR0334193
25 S Mac Lane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer (1998) MR1712872
26 I Madsen, Algebraic $K$–theory and traces, from: "Current developments in mathematics, 1995 (Cambridge, MA)" (editors R Bott, M Hopkins, A Jaffe, I Singer, D Stroock, S T Yau), Int. Press (1994) 191 MR1474979
27 M Mahowald, Ring spectra which are Thom complexes, Duke Math. J. 46 (1979) 549 MR544245
28 M Mahowald, D C Ravenel, P Shick, The Thomified Eilenberg-Moore spectral sequence, from: "Cohomological methods in homotopy theory (Bellaterra, 1998)" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 249 MR1851257
29 M Mahowald, N Ray, A note on the Thom isomorphism, Proc. Amer. Math. Soc. 82 (1981) 307 MR609673
30 M A Mandell, Topological Hochschild homology of an ${E}_n$ ring spectrum is ${E}_{n-1}$, Preprint (2004)
31 M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. $(3)$ 82 (2001) 441 MR1806878
32 J P May, The geometry of iterated loop spaces, Lectures Notes in Math. 271, Springer (1972) MR0420610
33 J P May, Classifying spaces and fibrations, Mem. Amer. Math. Soc. 155 (1975) MR0370579
34 J P May, $E_{\infty }$ ring spaces and $E_{\infty }$ ring spectra, Lecture Notes in Math. 577, Springer (1977) 268 MR0494077
35 J P May, Fibrewise localization and completion, Trans. Amer. Math. Soc. 258 (1980) 127 MR554323
36 J P May, J Sigurdsson, Parametrized homotopy theory, Math. Surveys and Monogr. 132, Amer. Math. Soc. (2006) MR2271789
37 J R Munkres, Topology: a first course, Prentice-Hall Inc. (2000) MR0464128
38 S Sagave, C Schlichtkrull, Diagram spaces and symmetric spectra, in preparation
39 C Schlichtkrull, Higher topological Hochschild homology of Thom spectra arXiv:0811.0597
40 C Schlichtkrull, Units of ring spectra and their traces in algebraic $K$–theory, Geom. Topol. 8 (2004) 645 MR2057776
41 C Schlichtkrull, The homotopy infinite symmetric product represents stable homotopy, Algebr. Geom. Topol. 7 (2007) 1963 MR2366183
42 C Schlichtkrull, Thom spectra that are symmetric spectra, Doc. Math. 14 (2009) 699 MR2578805
43 S Schwede, B E Shipley, Algebras and modules in monoidal model categories, Proc. London Math. Soc. $(3)$ 80 (2000) 491 MR1734325
44 G Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973) 213 MR0331377
45 G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
46 B Shipley, Symmetric spectra and topological Hochschild homology, $K$–Theory 19 (2000) 155 MR1740756
47 R E Stong, Notes on cobordism theory, Math. notes, Princeton Univ. Press (1968) MR0248858
48 A Strøm, The homotopy category is a homotopy category, Arch. Math. $($Basel$)$ 23 (1972) 435 MR0321082
49 R W Thomason, Uniqueness of delooping machines, Duke Math. J. 46 (1979) 217 MR534053
50 F Waldhausen, Algebraic $K$–theory of topological spaces. II, from: "Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, 1978)" (editors J L Dupont, I Madsen), Lecture Notes in Math. 763, Springer (1979) 356 MR561230
51 G W Whitehead, Elements of homotopy theory, Graduate Texts in Math. 61, Springer (1978) MR516508