Volume 19, issue 2 (2019)

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

Volume 19
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

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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7 M Bökstedt, Topological Hochschild homology, unpublished manuscript (1987)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