Algebraic & Geometric Topology Volume 16, issue 5 (2016)

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Function spaces and classifying spaces of algebras over a prop

Sinan Yalin

Algebraic & Geometric Topology 16 (2016) 2715–2749

DOI: 10.2140/agt.2016.16.2715

Bibliography

1	C Barwick, D M Kan, Relative categories: another model for the homotopy theory of homotopy theories, Indag. Math. 23 (2012) 42 MR2877401
2	J E Bergner, A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007) 2043 MR2276611
3	M Chas, D Sullivan, String topology, arXiv:math/9911159
4	M Chas, D Sullivan, Closed string operators in topology leading to Lie bialgebras and higher string algebra, from: "The legacy of Niels Henrik Abel" (editors O A Laudal, R Piene), Springer (2004) 771 MR2077595
5	I Ciocan-Fontanine, M M Kapranov, Derived Hilbert schemes, J. Amer. Math. Soc. 15 (2002) 787 MR1915819
6	V G Drinfel’d, Quantum groups, from: "Proceedings of the International Congress of Mathematicians, I, II" (editor A M Gleason), Amer. Math. Soc. (1987) 798 MR934283
7	V G Drinfel’d, On quasitriangular quasi-Hopf algebras and on a group that is closely connected with Gal(Q∕Q), Algebra i Analiz 2 (1990) 149 MR1080203
8	W G Dwyer, D M Kan, Calculating simplicial localizations, J. Pure Appl. Algebra 18 (1980) 17 MR578563
9	W G Dwyer, D M Kan, Function complexes in homotopical algebra, Topology 19 (1980) 427 MR584566
10	W G Dwyer, D M Kan, Simplicial localizations of categories, J. Pure Appl. Algebra 17 (1980) 267 MR579087
11	Y Frégier, M Markl, D Yau, The L_∞–deformation complex of diagrams of algebras, New York J. Math. 15 (2009) 353 MR2530153
12	B Fresse, Props in model categories and homotopy invariance of structures, Georgian Math. J. 17 (2010) 79 MR2640648
13	P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
14	M W Johnson, D Yau, On homotopy invariance for algebras over colored PROPs, J. Homotopy Relat. Struct. 4 (2009) 275 MR2559644
15	G M Kelly, Basic concepts of enriched category theory, 64, Cambridge Univ. Press (1982) 245 MR651714
16	J Kock, Frobenius algebras and 2D topological quantum field theories, 59, Cambridge Univ. Press (2004) MR2037238
17	M Markl, Homotopy algebras are homotopy algebras, Forum Math. 16 (2004) 129 MR2034546
18	M Markl, Intrinsic brackets and the L_∞–deformation theory of bialgebras, J. Homotopy Relat. Struct. 5 (2010) 177 MR2812919
19	S Merkulov, B Vallette, Deformation theory of representations of prop(erad)s, II, J. Reine Angew. Math. 636 (2009) 123 MR2572248
20	D Quillen, Higher algebraic K–theory, I, from: "Algebraic K–theory, I : Higher K–theories" (editor H Bass), Lecture Notes in Math. 341, Springer (1973) 85 MR0338129
21	C W Rezk, Spaces of algebra structures and cohomology of operads, PhD thesis, Massachusetts Institute of Technology (1996) MR2716655
22	C Rezk, A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001) 973 MR1804411
23	M Schlessinger, J Stasheff, The Lie algebra structure of tangent cohomology and deformation theory, J. Pure Appl. Algebra 38 (1985) 313 MR814187
24	V G Turaev, Skein quantization of Poisson algebras of loops on surfaces, Ann. Sci. École Norm. Sup. 24 (1991) 635 MR1142906
25	S Yalin, Classifying spaces of algebras over a prop, Algebr. Geom. Topol. 14 (2014) 2561 MR3276841
26	S Yalin, Simplicial localisation of homotopy algebras over a prop, Math. Proc. Cambridge Philos. Soc. 157 (2014) 457 MR3286518
27	S Yalin, Moduli stacks of algebraic structures and deformation theory, J. Noncommut. Geom. 10 (2016) 579 MR3519047