Volume 16, issue 4 (2012)

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
Rational algebraic $K$–theory of topological $K$–theory

Christian Ausoni and John Rognes

Geometry & Topology 16 (2012) 2037–2065
Bibliography
1 C Ausoni, Topological Hochschild homology of connective complex $K$–theory, Amer. J. Math. 127 (2005) 1261 MR2183525
2 C Ausoni, On the algebraic $K$–theory of the complex $K$–theory spectrum, Invent. Math. 180 (2010) 611 MR2609252
3 C Ausoni, B I Dundas, J Rognes, Divisibility of the Dirac magnetic monopole as a two-vector bundle over the three-sphere, Doc. Math. 13 (2008) 795 MR2466184
4 C Ausoni, J Rognes, Algebraic $K$–theory of topological $K$–theory, Acta Math. 188 (2002) 1 MR1947457
5 N A Baas, B I Dundas, B Richter, J Rognes, Stable bundles over rig categories, J. Topol. 4 (2011) 623 MR2832571
6 N A Baas, B I Dundas, J Rognes, Two-vector bundles and forms of elliptic cohomology, from: "Topology, geometry and quantum field theory", London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 18 MR2079370
7 A J Blumberg, M A Mandell, The localization sequence for the algebraic $K$–theory of topological $K$–theory, Acta Math. 200 (2008) 155 MR2413133
8 M Bökstedt, W C Hsiang, I Madsen, The cyclotomic trace and algebraic $K$–theory of spaces, Invent. Math. 111 (1993) 465 MR1202133
9 A Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. 7 (1974) 235 MR0387496
10 M Brun, Z Fiedorowicz, R M Vogt, On the multiplicative structure of topological Hochschild homology, Algebr. Geom. Topol. 7 (2007) 1633 MR2366174
11 J L Brylinski, Loop spaces, characteristic classes and geometric quantization, Progress in Mathematics 107, Birkhäuser (1993) MR1197353
12 R L Cohen, J D S Jones, Algebraic $K$–theory of spaces and the Novikov conjecture, Topology 29 (1990) 317 MR1066175
13 B I Dundas, The cyclotomic trace for $S$–algebras, J. London Math. Soc. 70 (2004) 659 MR2096869
14 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
15 T G Goodwillie, Relative algebraic $K$–theory and cyclic homology, Ann. of Math. 124 (1986) 347 MR855300
16 L Hesselholt, On the $p$–typical curves in Quillen's $K$–theory, Acta Math. 177 (1996) 1 MR1417085
17 L Hesselholt, I Madsen, On the $K$–theory of local fields, Ann. of Math. 158 (2003) 1 MR1998478
18 M J Hopkins, Algebraic topology and modular forms, from: "Proceedings of the International Congress of Mathematicians, Vol I (Beijing, 2002)", Higher Ed. Press (2002) 291 MR1989190
19 M Hovey, B Shipley, J Smith, Symmetric spectra, J. Amer. Math. Soc. 13 (2000) 149 MR1695653
20 W C Hsiang, R E Staffeldt, A model for computing rational algebraic $K$–theory of simply connected spaces, Invent. Math. 68 (1982) 227 MR666160
21 I Kříž, J P May, Operads, algebras, modules and motives, Astérisque 233 (1995) MR1361938
22 P S Landweber, D C Ravenel, R E Stong, Periodic cohomology theories defined by elliptic curves, from: "The Čech centennial (Boston, MA, 1993)", Contemp. Math. 181, Amer. Math. Soc. (1995) 317 MR1320998
23 M A Mandell, Topological André–Quillen cohomology and $E_\infty$ André–Quillen cohomology, Adv. Math. 177 (2003) 227 MR1990939
24 M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001) 441 MR1806878
25 J P May, $E_{\infty }$ ring spaces and $E_{\infty }$ ring spectra, Lecture Notes in Mathematics 577, Springer (1977) MR0494077
26 J W Milnor, J C Moore, On the structure of Hopf algebras, Ann. of Math. 81 (1965) 211 MR0174052
27 G Moore, $K$–theory from a physical perspective, from: "Topology, geometry and quantum field theory", London Math. Soc. Lecture Note Ser. 308, Cambridge Univ. Press (2004) 194 MR2079376
28 J Rognes, Trace maps from the algebraic $K$–theory of the integers (after Marcel Bökstedt), J. Pure Appl. Algebra 125 (1998) 277 MR1600028
29 J Rognes, Galois extensions of structured ring spectra. Stably dualizable groups, Mem. Amer. Math. Soc. 192 (2008) MR2387923
30 C Schlichtkrull, Units of ring spectra and their traces in algebraic $K$–theory, Geom. Topol. 8 (2004) 645 MR2057776
31 S Schwede, Stable homotopical algebra and $\Gamma$–spaces, Math. Proc. Cambridge Philos. Soc. 126 (1999) 329 MR1670249
32 G Segal, Elliptic cohomology (after Landweber–Stong, Ochanine, Witten, and others), from: "Séminaire Bourbaki 1987/88", Astérisque 161–162 (1988) 187 MR992209
33 B Toën, G Vezzosi, Brave new algebraic geometry and global derived moduli spaces of ring spectra, from: "Elliptic cohomology", London Math. Soc. Lecture Note Ser. 342, Cambridge Univ. Press (2007) 325 MR2330521
34 F Waldhausen, Algebraic $K$–theory of topological spaces I, from: "Algebraic and geometric topology (Proc. Sympos. Pure Math., Stanford Univ., Stanford, Calif., 1976), Part 1", Proc. Sympos. Pure Math. XXXII, Amer. Math. Soc. (1978) 35 MR520492
35 F Waldhausen, Algebraic $K$–theory of spaces, a manifold approach, from: "Current trends in algebraic topology, Part 1 (London, Ont., 1981)", CMS Conf. Proc. 2, Amer. Math. Soc. (1982) 141 MR686115
36 F Waldhausen, Algebraic $K$–theory of spaces, from: "Algebraic and geometric topology (New Brunswick, N.J., 1983)", Lecture Notes in Math. 1126, Springer (1985) 318 MR802796
37 F Waldhausen, On the construction of the Kan loop group, Doc. Math. 1 (1996) 121 MR1386050