Volume 19, issue 2 (2019)

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

Volume 24
Issue 9, 4731–5219
Issue 8, 4139–4730
Issue 7, 3571–4137
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

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

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Topological Hochschild homology and higher characteristics

Jonathan A Campbell and Kate Ponto

Algebraic & Geometric Topology 19 (2019) 965–1017
Bibliography
1 M F Atiyah, I M Singer, The index of elliptic operators, I, Ann. of Math. 87 (1968) 484 MR0236950
2 C Barwick, On the algebraic K–theory of higher categories, J. Topol. 9 (2016) 245 MR3465850
3 J Bénabou, Introduction to bicategories, from: "Reports of the Midwest Category Seminar", Springer (1967) 1 MR0220789
4 S Bentzen, I Madsen, Trace maps in algebraic K–theory and the Coates–Wiles homomorphism, J. Reine Angew. Math. 411 (1990) 171 MR1072979
5 A J Blumberg, D Gepner, G Tabuada, A universal characterization of higher algebraic K–theory, Geom. Topol. 17 (2013) 733 MR3070515
6 A J Blumberg, M A Mandell, Localization theorems in topological Hochschild homology and topological cyclic homology, Geom. Topol. 16 (2012) 1053 MR2928988
7 M Bökstedt, Topological Hochschild homology, unpublished manuscript (1987)
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 Dold, Fixed point index and fixed point theorem for Euclidean neighborhood retracts, Topology 4 (1965) 1 MR0193634
10 A Dold, D Puppe, Duality, trace, and transfer, from: "Proceedings of the international conference on geometric topology" (editors K Borsuk, A Kirkor), PWN (1980) 81 MR656721
11 B I Dundas, R McCarthy, Topological Hochschild homology of ring functors and exact categories, J. Pure Appl. Algebra 109 (1996) 231 MR1388700
12 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
13 S Gen-hua, On least number of fixed points and Nielsen numbers, Chinese Math.–Acta 8 (1966) 234 MR0210109
14 T G Goodwillie, Cyclic homology, derivations, and the free loopspace, Topology 24 (1985) 187 MR793184
15 A Hattori, Rank element of a projective module, Nagoya Math. J. 25 (1965) 113 MR0175950
16 Y Iwashita, The Lefschetz–Reidemeister trace in algebraic K–theory, PhD thesis, University of Illinois at Urbana-Champaign (1999) MR2699742
17 D Kaledin, Trace theories and localization, from: "Stacks and categories in geometry, topology, and algebra" (editors T Pantev, C Simpson, B Toën, M Vaquié, G Vezzosi), Contemp. Math. 643, Amer. Math. Soc. (2015) 227 MR3381474
18 T Leinster, Basic bicategories, preprint (1998) arXiv:math/9810017
19 J A Lind, C Malkiewich, The Morita equivalence between parametrized spectra and module spectra, from: "New directions in homotopy theory", Contemp. Math. 707, Amer. Math. Soc. (2018) 45 MR3807741
20 J A Lind, C Malkiewich, The transfer map of free loop spaces, Trans. Amer. Math. Soc. 371 (2019) 2503 MR3896088
21 M A Mandell, J P May, S Schwede, B Shipley, Model categories of diagram spectra, Proc. London Math. Soc. 82 (2001) 441 MR1806878
22 J P May, J Sigurdsson, Parametrized homotopy theory, 132, Amer. Math. Soc. (2006) MR2271789
23 K Ponto, Fixed point theory and trace for bicategories, 333, Soc. Math. France (2010) MR2741967
24 K Ponto, Coincidence invariants and higher Reidemeister traces, J. Fixed Point Theory Appl. 18 (2016) 147 MR3463529
25 K Ponto, M Shulman, Duality and traces for indexed monoidal categories, Theory Appl. Categ. 26 (2012) 582 MR3065938
26 K Ponto, M Shulman, Shadows and traces in bicategories, J. Homotopy Relat. Struct. 8 (2013) 151 MR3095324
27 K Ponto, M Shulman, The multiplicativity of fixed point invariants, Algebr. Geom. Topol. 14 (2014) 1275 MR3190594
28 C Schlichtkrull, The transfer map in topological Hochschild homology, J. Pure Appl. Algebra 133 (1998) 289 MR1654263
29 C Schlichtkrull, Transfer maps and the cyclotomic trace, Math. Ann. 336 (2006) 191 MR2242623
30 S Schwede, B Shipley, Equivalences of monoidal model categories, Algebr. Geom. Topol. 3 (2003) 287 MR1997322
31 G Segal, Categories and cohomology theories, Topology 13 (1974) 293 MR0353298
32 M Shulman, Framed bicategories and monoidal fibrations, Theory Appl. Categ. 20 (2008) 650 MR2534210
33 J Stallings, Centerless groups : an algebraic formulation of Gottlieb’s theorem, Topology 4 (1965) 129 MR0202807
34 F Waldhausen, Algebraic K–theory of spaces, from: "Algebraic and geometric topology" (editors A Ranicki, N Levitt, F Quinn), Lecture Notes in Math. 1126, Springer (1985) 318 MR802796
35 F Wecken, Fixpunktklassen, I, Math. Ann. 117 (1941) 659 MR0005339