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Vanishing theorems for representation homology and the derived cotangent complex

Yuri Berest, Ajay C Ramadoss and Wai-kit Yeung

Algebraic & Geometric Topology 19 (2019) 281–339
Bibliography
1 M André, Homologie des algèbres commutatives, 206, Springer (1974) MR0352220
2 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
3 Y Berest, G Felder, A Ramadoss, Derived representation schemes and noncommutative geometry, from: "Expository lectures on representation theory" (editors K Igusa, A Martsinkovsky, G Todorov), Contemp. Math. 607, Amer. Math. Soc. (2014) 113 MR3204869
4 Y Berest, G Khachatryan, A Ramadoss, Derived representation schemes and cyclic homology, Adv. Math. 245 (2013) 625 MR3084440
5 Y Berest, A Ramadoss, Stable representation homology and Koszul duality, J. Reine Angew. Math. 715 (2016) 143 MR3507922
6 Y Berest, A C Ramadoss, W k Yeung, Representation homology of spaces and higher Hochschild homology, preprint (2017) arXiv:1703.03505
7 A K Bousfield, D M Kan, Homotopy limits, completions and localizations, 304, Springer (1972) MR0365573
8 A K Bousfield, D M Kan, The homotopy spectral sequence of a space with coefficients in a ring, Topology 11 (1972) 79 MR0283801
9 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
10 H Cartan, S Eilenberg, Homological algebra, Princeton Univ. Press (1956) MR0077480
11 I Ciocan-Fontanine, M Kapranov, Virtual fundamental classes via dg–manifolds, Geom. Topol. 13 (2009) 1779 MR2496057
12 F R Cohen, M Stafa, A survey on spaces of homomorphisms to Lie groups, from: "Configuration spaces" (editors F Callegaro, F Cohen, C De Concini, E M Feichtner, G Gaiffi, M Salvetti), Springer INdAM Ser. 14, Springer (2016) 361 MR3615740
13 M Culler, P B Shalen, Varieties of group representations and splittings of 3–manifolds, Ann. of Math. 117 (1983) 109 MR683804
14 J Cuntz, D Quillen, Algebra extensions and nonsingularity, J. Amer. Math. Soc. 8 (1995) 251 MR1303029
15 W G Dwyer, J Spaliński, Homotopy theories and model categories, from: "Handbook of algebraic topology" (editor I M James), North-Holland (1995) 73 MR1361887
16 P G Goerss, J F Jardine, Simplicial homotopy theory, 174, Birkhäuser (1999) MR1711612
17 W M Goldman, The symplectic nature of fundamental groups of surfaces, Adv. in Math. 54 (1984) 200 MR762512
18 W M Goldman, Representations of fundamental groups of surfaces, from: "Geometry and topology" (editors J Alexander, J Harer), Lecture Notes in Math. 1167, Springer (1985) 95 MR827264
19 K Habiro, On the category of finitely generated free groups, preprint (2016) arXiv:1609.06599
20 D K Harrison, Commutative algebras and cohomology, Trans. Amer. Math. Soc. 104 (1962) 191 MR0142607
21 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
22 S Iyengar, André–Quillen homology of commutative algebras, from: "Interactions between homotopy theory and algebra" (editors L L Avramov, J D Christensen, W G Dwyer, M A Mandell, B E Shipley), Contemp. Math. 436, Amer. Math. Soc. (2007) 203 MR2355775
23 D Johnson, J J Millson, Deformation spaces associated to compact hyperbolic manifolds, from: "Discrete groups in geometry and analysis" (editor R Howe), Progr. Math. 67, Birkhäuser (1987) 48 MR900823
24 D M Kan, A combinatorial definition of homotopy groups, Ann. of Math. 67 (1958) 282 MR0111032
25 D M Kan, On homotopy theory and c.s.s. groups, Ann. of Math. 68 (1958) 38 MR0111033
26 D M Kan, A relation between CW–complexes and free c.s.s. groups, Amer. J. Math. 81 (1959) 512 MR0111036
27 M Kapranov, Injective resolutions of BG and derived moduli spaces of local systems, J. Pure Appl. Algebra 155 (2001) 167 MR1801413
28 L Le Bruyn, Qurves and quivers, J. Algebra 290 (2005) 447 MR2153263
29 J L Loday, Cyclic homology, 301, Springer (1998) MR1600246
30 A Lubotzky, A R Magid, Varieties of representations of finitely generated groups, 336, Amer. Math. Soc. (1985) MR818915
31 J Lurie, Derived algebraic geometry, PhD thesis, Massachusetts Institute of Technology (2004) MR2717174
32 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
33 J P May, Simplicial objects in algebraic topology, 11, Van Nostrand (1967) MR0222892
34 T Pantev, B Toën, M Vaquié, G Vezzosi, Shifted symplectic structures, Publ. Math. Inst. Hautes Études Sci. 117 (2013) 271 MR3090262
35 T Pirashvili, Hodge decomposition for higher order Hochschild homology, Ann. Sci. École Norm. Sup. 33 (2000) 151 MR1755114
36 J P Pridham, Pro-algebraic homotopy types, Proc. Lond. Math. Soc. 97 (2008) 273 MR2439664
37 J P Pridham, Constructing derived moduli stacks, Geom. Topol. 17 (2013) 1417 MR3073928
38 J P Pridham, Presenting higher stacks as simplicial schemes, Adv. Math. 238 (2013) 184 MR3033634
39 D G Quillen, Homotopical algebra, 43, Springer (1967) MR0223432
40 D Quillen, Rational homotopy theory, Ann. of Math. 90 (1969) 205 MR0258031
41 D Quillen, On the (co)homology of commutative rings, from: "Applications of categorical algebra" (editor A Heller), Amer. Math. Soc. (1970) 65 MR0257068
42 R W Richardson, Commuting varieties of semisimple Lie algebras and algebraic groups, Compositio Math. 38 (1979) 311 MR535074
43 S Schwede, Spectra in model categories and applications to the algebraic cotangent complex, J. Pure Appl. Algebra 120 (1997) 77 MR1466099
44 P B Shalen, Representations of 3–manifold groups, from: "Handbook of geometric topology" (editors R J Daverman, R B Sher), North-Holland (2002) 955 MR1886685
45 A S Sikora, Character varieties, Trans. Amer. Math. Soc. 364 (2012) 5173 MR2931326
46 S Thomas, The functors W and Diag Nerve are simplicially homotopy equivalent, J. Homotopy Relat. Struct. 3 (2008) 359 MR2481463
47 R W Thomason, Une formule de Lefschetz en K–théorie équivariante algébrique, Duke Math. J. 68 (1992) 447 MR1194949
48 B Toën, Derived algebraic geometry, EMS Surv. Math. Sci. 1 (2014) 153 MR3285853
49 B Toën, Derived algebraic geometry and deformation quantization, from: "Proceedings of the International Congress of Mathematicians" (editors S Y Jang, Y R Kim, D W Lee, I Ye), Kyung Moon Sa (2014) 769 MR3728637
50 B Toën, G Vezzosi, Homotopical algebraic geometry, I : Topos theory, Adv. Math. 193 (2005) 257 MR2137288
51 B Toën, G Vezzosi, Homotopical algebraic geometry, II : Geometric stacks and applications, 902, Amer. Math. Soc. (2008) MR2394633
52 C A Weibel, An introduction to homological algebra, 38, Cambridge Univ. Press (1994) MR1269324
53 A Weil, Remarks on the cohomology of groups, Ann. of Math. 80 (1964) 149 MR0169956
54 W k Yeung, Representation homology and knot contact homology, PhD thesis, Cornell University (2017) MR3755079