Volume 19, issue 3 (2019)

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

Volume 24
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
$C^*$–algebraic drawings of dendroidal sets

Snigdhayan Mahanta

Algebraic & Geometric Topology 19 (2019) 1171–1206
Bibliography
1 J Adámek, J Rosický, Locally presentable and accessible categories, 189, Cambridge Univ. Press (1994) MR1294136
2 I Barnea, M Joachim, S Mahanta, Model structure on projective systems of C–algebras and bivariant homology theories, New York J. Math. 23 (2017) 383 MR3649664
3 I Barnea, T M Schlank, A projective model structure on pro-simplicial sheaves, and the relative étale homotopy type, Adv. Math. 291 (2016) 784 MR3459031
4 C Barwick, D M Kan, Relative categories: another model for the homotopy theory of homotopy theories, Indag. Math. 23 (2012) 42 MR2877401
5 M Bašić, T Nikolaus, Dendroidal sets as models for connective spectra, J. K–Theory 14 (2014) 387 MR3349322
6 C Berger, I Moerdijk, Axiomatic homotopy theory for operads, Comment. Math. Helv. 78 (2003) 805 MR2016697
7 A J Blumberg, D Gepner, G Tabuada, A universal characterization of higher algebraic K–theory, Geom. Topol. 17 (2013) 733 MR3070515
8 J M Boardman, R M Vogt, Homotopy invariant algebraic structures on topological spaces, 347, Springer (1973) MR0420609
9 D C Cisinski, Les préfaisceaux comme modèles des types d’homotopie, 308, Soc. Mat. de France (2006) MR2294028
10 D C Cisinski, I Moerdijk, Dendroidal sets as models for homotopy operads, J. Topol. 4 (2011) 257 MR2805991
11 D C Cisinski, I Moerdijk, Dendroidal Segal spaces and –operads, J. Topol. 6 (2013) 675 MR3100887
12 D C Cisinski, I Moerdijk, Dendroidal sets and simplicial operads, J. Topol. 6 (2013) 705 MR3100888
13 A Connes, Noncommutative geometry, Academic (1994) MR1303779
14 A Connes, M Marcolli, Noncommutative geometry, quantum fields and motives, 55, Amer. Math. Soc. (2008) MR2371808
15 G Cortiñas, N C Phillips, Algebraic K–theory and properly infinite C–algebras, preprint (2014) arXiv:1402.3197
16 J Cuntz, Noncommutative simplicial complexes and the Baum–Connes conjecture, Geom. Funct. Anal. 12 (2002) 307 MR1911662
17 J Cuntz, Bivariant K– and cyclic theories, from: "Handbook of K–theory" (editors E M Friedlander, D R Grayson), Springer (2005) 655 MR2181832
18 W G Dwyer, D M Kan, Function complexes in homotopical algebra, Topology 19 (1980) 427 MR584566
19 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
20 G Heuts, An infinite loop space machine for –operads, preprint (2011) arXiv:1112.0625
21 G Heuts, V Hinich, I Moerdijk, On the equivalence between Lurie’s model and the dendroidal model for infinity-operads, Adv. Math. 302 (2016) 869 MR3545944
22 V Hinich, Dwyer–Kan localization revisited, Homology Homotopy Appl. 18 (2016) 27 MR3460765
23 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
24 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
25 B Keller, On differential graded categories, from: "International Congress of Mathematicians, II" (editors M Sanz-Solé, J Soria, J L Varona, J Verdera), Eur. Math. Soc. (2006) 151 MR2275593
26 E Kirchberg, N C Phillips, Embedding of exact C–algebras in the Cuntz algebra 𝒪2, J. Reine Angew. Math. 525 (2000) 17 MR1780426
27 M Kontsevich, XI Solomon Lefschetz memorial lecture series : Hodge structures in non-commutative geometry, from: "Non-commutative geometry in mathematics and physics" (editors G Dito, H García-Compeán, E Lupercio, F J Turrubiates), Contemp. Math. 462, Amer. Math. Soc. (2008) 1 MR2444365
28 A Kumjian, D Pask, I Raeburn, Cuntz–Krieger algebras of directed graphs, Pacific J. Math. 184 (1998) 161 MR1626528
29 J L Loday, B Vallette, Algebraic operads, 346, Springer (2012) MR2954392
30 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
31 J Lurie, Higher algebra, book project (2011)
32 S Mac Lane, I Moerdijk, Sheaves in geometry and logic: a first introduction to topos theory, Springer (1994) MR1300636
33 S Mahanta, Noncommutative correspondence categories, simplicial sets and pro C–algebras, preprint (2009) arXiv:0906.5400
34 S Mahanta, Noncommutative geometry in the framework of differential graded categories, from: "Arithmetic and geometry around quantization" (editors Ö Ceyhan, Y I Manin, M Marcolli), Progr. Math. 279, Birkhäuser (2010) 253 MR2656948
35 S Mahanta, Algebraic K–theory, K–regularity, and 𝕋–duality of 𝒪–stable C–algebras, Math. Phys. Anal. Geom. 18 (2015) 21 MR3338702
36 S Mahanta, Colocalizations of noncommutative spectra and bootstrap categories, Adv. Math. 285 (2015) 72 MR3406496
37 S Mahanta, Noncommutative stable homotopy and stable infinity categories, J. Topol. Anal. 7 (2015) 135 MR3284393
38 S Mahanta, Symmetric monoidal noncommutative spectra, strongly self-absorbing C–algebras, and bivariant homology, J. Noncommut. Geom. 10 (2016) 1269 MR3597145
39 Y I Manin, Moduli, motives, mirrors, from: "European Congress of Mathematics, I" (editors C Casacuberta, R M Miró-Roig, J Verdera, S Xambó-Descamps), Progr. Math. 201, Birkhäuser (2001) 53 MR1905313
40 M Markl, S Shnider, J Stasheff, Operads in algebra, topology and physics, 96, Amer. Math. Soc. (2002) MR1898414
41 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR0420610
42 A Mazel-Gee, Quillen adjunctions induce adjunctions of quasicategories, New York J. Math. 22 (2016) 57 MR3484677
43 I Moerdijk, Lectures on dendroidal sets, from: "Simplicial methods for operads and algebraic geometry" (editors C Casacuberta, J Kock), Springer (2010) 1 MR2778589
44 I Moerdijk, I Weiss, Dendroidal sets, Algebr. Geom. Topol. 7 (2007) 1441 MR2366165
45 I Moerdijk, I Weiss, On inner Kan complexes in the category of dendroidal sets, Adv. Math. 221 (2009) 343 MR2508925
46 T Nikolaus, Algebraic K–theory of –operads, J. K–Theory 14 (2014) 614 MR3349328
47 P A Østvær, Homotopy theory of C–algebras, Springer (2010) 139 MR2723902
48 D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
49 I Raeburn, Graph algebras, 103, Amer. Math. Soc. (2005) MR2135030
50 G Tabuada, A guided tour through the garden of noncommutative motives, from: "Topics in noncommutative geometry" (editor G Cortiñas), Clay Math. Proc. 16, Amer. Math. Soc. (2012) 259 MR2986869
51 I. Weiss, Dendroidal sets, PhD thesis, Utrecht University (2007)