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

Volume 26
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Derived character maps of group representations

Yuri Berest and Ajay C Ramadoss

Algebraic & Geometric Topology 24 (2024) 4991–5044
Bibliography
1 G Arone, M Ching, Goodwillie calculus, from: "Handbook of homotopy theory", CRC Press (2020) 1 MR4197981
2 S V Ault, Symmetric homology of algebras, Algebr. Geom. Topol. 10 (2010) 2343 MR2748335
3 S V Ault, Homology operations in symmetric homology, Homology Homotopy Appl. 16 (2014) 239 MR3263894
4 B Badzioch, Algebraic theories in homotopy theory, Ann. of Math. 155 (2002) 895 MR1923968
5 H J Baues, Homotopy types, from: "Handbook of algebraic topology", North-Holland (1995) 1 MR1361886
6 Y Berest, X Chen, F Eshmatov, A Ramadoss, Noncommutative Poisson structures, derived representation schemes and Calabi–Yau algebras, from: "Mathematical aspects of quantization", Contemp. Math. 583, Amer. Math. Soc. (2012) 219 MR3013096
7 Y Berest, G Felder, S Patotski, A C Ramadoss, T Willwacher, Chern–Simons forms and higher character maps of Lie representations, Int. Math. Res. Not. 2017 (2017) 158 MR3632101
8 Y Berest, G Felder, S Patotski, A C Ramadoss, T Willwacher, Representation homology, Lie algebra cohomology and the derived Harish-Chandra homomorphism, J. Eur. Math. Soc. 19 (2017) 2811 MR3692888
9 Y Berest, G Khachatryan, A Ramadoss, Derived representation schemes and cyclic homology, Adv. Math. 245 (2013) 625 MR3084440
10 Y Berest, A C Ramadoss, Homotopy algebras and functor homology, in preparation
11 Y Berest, A Ramadoss, Stable representation homology and Koszul duality, J. Reine Angew. Math. 715 (2016) 143 MR3507922
12 Y Berest, A C Ramadoss, W K Yeung, Vanishing theorems for representation homology and the derived cotangent complex, Algebr. Geom. Topol. 19 (2019) 281 MR3910582
13 Y Berest, A C Ramadoss, W K Yeung, Representation homology of simply connected spaces, J. Topol. 15 (2022) 692 MR4441602
14 Y Berest, A C Ramadoss, W K Yeung, Representation homology of topological spaces, Int. Math. Res. Not. 2022 (2022) 4093 MR4391884
15 Y Berest, A C Ramadoss, Y Zhang, Dual Hodge decompositions and derived Poisson brackets, Selecta Math. 23 (2017) 2029 MR3663602
16 Y Berest, A C Ramadoss, Y Zhang, Hodge decomposition of string topology, Forum Math. Sigma 9 (2021) MR4247639
17 J E Bergner, Rigidification of algebras over multi-sorted theories, Algebr. Geom. Topol. 6 (2006) 1925 MR2263055
18 G Biedermann, W G Dwyer, Homotopy nilpotent groups, Algebr. Geom. Topol. 10 (2010) 33 MR2580428
19 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR365573
20 D Burghelea, Z Fiedorowicz, Cyclic homology and algebraic K–theory of spaces, II, Topology 25 (1986) 303 MR842427
21 G E Carlsson, R L Cohen, The cyclic groups and the free loop space, Comment. Math. Helv. 62 (1987) 423 MR910170
22 G Carlsson, R J Milgram, Stable homotopy and iterated loop spaces, from: "Handbook of algebraic topology", North-Holland (1995) 505 MR1361898
23 W Chachólski, J Scherer, Homotopy theory of diagrams, 736, Amer. Math. Soc. (2002) MR1879153
24 D C Cisinski, Images directes cohomologiques dans les catégories de modèles, Ann. Math. Blaise Pascal 10 (2003) 195 MR2031269
25 A Connes, Cohomologie cyclique et foncteurs Extn, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983) 953 MR777584
26 A Djament, Décomposition de Hodge pour l’homologie stable des groupes d’automorphismes des groupes libres, Compos. Math. 155 (2019) 1794 MR3993804
27 A Djament, T Pirashvili, C Vespa, Cohomologie des foncteurs polynomiaux sur les groupes libres, Doc. Math. 21 (2016) 205 MR3505136
28 A Djament, C Vespa, Sur l’homologie des groupes d’automorphismes des groupes libres à coefficients polynomiaux, Comment. Math. Helv. 90 (2015) 33 MR3317332
29 Z Fiedorowicz, Classifying spaces of topological monoids and categories, Amer. J. Math. 106 (1984) 301 MR737777
30 Z Fiedorowicz, Symmetric bar construction, preprint (1991)
31 Z Fiedorowicz, J L Loday, Crossed simplicial groups and their associated homology, Trans. Amer. Math. Soc. 326 (1991) 57 MR998125
32 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
33 T G Goodwillie, Cyclic homology, derivations, and the free loopspace, Topology 24 (1985) 187 MR793184
34 T G Goodwillie, Calculus, I : The first derivative of pseudoisotopy theory, K–Theory 4 (1990) 1 MR1076523
35 T G Goodwillie, Calculus, II : Analytic functors, K–Theory 5 (1992) 295 MR1162445
36 T G Goodwillie, Calculus, III : Taylor series, Geom. Topol. 7 (2003) 645 MR2026544
37 D Graves, Hyperoctahedral homology for involutive algebras, Homology Homotopy Appl. 24 (2022) 1 MR4344317
38 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
39 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
40 M Hovey, Model categories, 63, Amer. Math. Soc. (1999) MR1650134
41 B Johnson, The derivatives of homotopy theory, Trans. Amer. Math. Soc. 347 (1995) 1295 MR1297532
42 D M Kan, On homotopy theory and c.s.s. groups, Ann. of Math. 68 (1958) 38 MR111033
43 M Kapranov, Injective resolutions of BG and derived moduli spaces of local systems, J. Pure Appl. Algebra 155 (2001) 167 MR1801413
44 M Kassabov, S Patotski, Character varieties as a tensor product, J. Algebra 500 (2018) 569 MR3765469
45 N J Kuhn, Goodwillie towers and chromatic homotopy: an overview, from: "Proceedings of the Nishida Fest", Geom. Topol. Monogr. 10, Geom. Topol. Publ. (2007) 245 MR2402789
46 P Lambrechts, D Stanley, Poincaré duality and commutative differential graded algebras, Ann. Sci. École Norm. Sup. 41 (2008) 495 MR2489632
47 J L Loday, Cyclic homology, 301, Springer (1998) MR1600246
48 J L Loday, Free loop space and homology, from: "Free loop spaces in geometry and topology", IRMA Lect. Math. Theor. Phys. 24, Eur. Math. Soc. (2015) 137 MR3444364
49 J L Loday, D Quillen, Cyclic homology and the Lie algebra homology of matrices, Comment. Math. Helv. 59 (1984) 569 MR780077
50 A Lubotzky, A R Magid, Varieties of representations of finitely generated groups, 336, Amer. Math. Soc. (1985) MR818915
51 S Mac Lane, Categories for the working mathematician, 5, Springer (1971) MR354798
52 J P May, The geometry of iterated loop spaces, 271, Springer (1972) MR420610
53 M C McCord, Classifying spaces and infinite symmetric products, Trans. Amer. Math. Soc. 146 (1969) 273 MR251719
54 T Pantev, B Toën, Poisson geometry of the moduli of local systems on smooth varieties, Publ. Res. Inst. Math. Sci. 57 (2021) 959 MR4322004
55 T Pantev, B Toën, M Vaquié, G Vezzosi, Shifted symplectic structures, Publ. Math. Inst. Hautes Études Sci. 117 (2013) 271 MR3090262
56 T Pirashvili, On the PROP corresponding to bialgebras, Cah. Topol. Géom. Différ. Catég. 43 (2002) 221 MR1928233
57 T Pirashvili, B Richter, Hochschild and cyclic homology via functor homology, K–Theory 25 (2002) 39 MR1899698
58 J P Pridham, Constructing derived moduli stacks, Geom. Topol. 17 (2013) 1417 MR3073928
59 C Procesi, The invariant theory of n × n matrices, Adv. Math. 19 (1976) 306 MR419491
60 D Quillen, Rational homotopy theory, Ann. of Math. 90 (1969) 205 MR258031
61 D Quillen, Higher algebraic K–theory, I, from: "Algebraic K–theory, I : Higher K–theories", Lecture Notes in Math. 341, Springer (1973) 85 MR338129
62 B Richter, From categories to homotopy theory, 188, Cambridge Univ. Press (2020) MR4411367
63 J Rosický, Rigidification of algebras over essentially algebraic theories, Appl. Categ. Structures 23 (2015) 159 MR3318284
64 S Schwede, B Shipley, Equivalences of monoidal model categories, Algebr. Geom. Topol. 3 (2003) 287 MR1997322
65 J P Serre, Lie algebras and Lie groups, Benjamin (1965) MR218496
66 A S Sikora, Character varieties, Trans. Amer. Math. Soc. 364 (2012) 5173 MR2931326
67 R W Thomason, Homotopy colimits in the category of small categories, Math. Proc. Cambridge Philos. Soc. 85 (1979) 91 MR510404
68 B Toën, Derived algebraic geometry, EMS Surv. Math. Sci. 1 (2014) 153 MR3285853
69 B Toën, G Vezzosi, Homotopical algebraic geometry, II : Geometric stacks and applications, 902, Amer. Math. Soc. (2008) MR2394633
70 B L Tsygan, Homology of matrix Lie algebras over rings and the Hochschild homology, Uspekhi Mat. Nauk 38 (1983) 217 MR695483
71 C Vespa, Extensions between functors from free groups, Bull. Lond. Math. Soc. 50 (2018) 401 MR3829729
72 F Waldhausen, Algebraic K–theory of topological spaces, I, from: "Algebraic and geometric topology, I", Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 35 MR520492
73 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
74 K Werndli, Double homotopy (co)limits for relative categories, from: "An alpine bouquet of algebraic topology", Contemp. Math. 708, Amer. Math. Soc. (2018) 275 MR3807759