@book{AST_2012__343__R1_0, author = {Behrend, Kai and Ginot, Gr\'egory and Noohi, Behrang and Xu, Ping}, title = {String topology for stacks}, series = {Ast\'erisque}, publisher = {Soci\'et\'e math\'ematique de France}, number = {343}, year = {2012}, zbl = {1253.55007}, mrnumber = {2977576}, language = {en}, url = {http://www.numdam.org/item/AST_2012__343__R1_0/} }
TY - BOOK AU - Behrend, Kai AU - Ginot, Grégory AU - Noohi, Behrang AU - Xu, Ping TI - String topology for stacks T3 - Astérisque PY - 2012 DA - 2012/// IS - 343 PB - Société mathématique de France UR - http://www.numdam.org/item/AST_2012__343__R1_0/ UR - https://zbmath.org/?q=an%3A1253.55007 UR - https://www.ams.org/mathscinet-getitem?mr=2977576 LA - en ID - AST_2012__343__R1_0 ER -
Behrend, Kai; Ginot, Grégory; Noohi, Behrang; Xu, Ping. String topology for stacks. Astérisque, no. 343 (2012), 183 p. http://numdam.org/item/AST_2012__343__R1_0/
[1] String topology of Poincaré duality groups", in Groups, homotopy and configuration spaces, Geom. Topol. Monogr., vol. 13, 2008, p. 1-10. | MR 2508199 | Zbl 1141.55004
, & - "[2] String bracket and flat connections", Algebr. Geom. Topol 7 (2007), p. 197-231. | Article | MR 2308942 | Zbl 1142.55006
& - "[3] Two-dimensional topological quantum field theories and Frobenius algebras", J. Knot Theory Ramifications 5 (1996), p. 569-587. | Article | MR 1414088 | Zbl 0897.57015
- "[4] The moment map and equivariant cohomology", Topology 23 (1984), p. 1-28. | Article | MR 721448 | Zbl 0521.58025
& - "[5] Group representations, -rings and the -homomorphism", Topology 8 (1969), p. 253-297. | Article | MR 244387 | Zbl 0159.53301
& - "[6] Cohomology of stacks", in Intersection theory and moduli, ICTP Lect. Notes, XIX, Abdus Salam Int. Cent. Theoret. Phys., Trieste, 2004, p. 249-294. | MR 2172499 | Zbl 1081.58003
- "[7] String topology for loop stacks", C. R. Math. Acad. Sci. Paris 344 (2007), p. 247-252. | Article | MR 2292996 | Zbl 1113.14005
, , & - "[8] Differentiable stacks and gerbes", J. Symplectic Geometry 9 (2011), p. 285-341. | Article | MR 2817778 | Zbl 1227.14007
& - "[9] Representations and cohomology. I, second ed., Cambridge Studies in Advanced Math., vol. 30, Cambridge Univ. Press, 1998. | Zbl 0908.20001
-[10] Heat kernels and Dirac operators, Grund. Math. Wiss., vol. 298, Springer, 1992. | MR 2273508 | Zbl 0744.58001
, & -[11] Introduction to compact transformation groups, Pure and Applied Mathematics, vol. 46, Academic Press, 1972. | MR 413144 | Zbl 0246.57017
-[12] Loop spaces, characteristic classes and geometric quantization, Progress in Math., vol. 107, Birkhäuser, 1993. | MR 1197353 | Zbl 0823.55002
-[13] Topological field theory interpretation of string topology", Comm. Math. Phys. 240 (2003), p. 397-421. | Article | MR 2005849 | Zbl 1052.81095
, & - "[14] String topology", preprint arXiv:GT/9911159. | Zbl 1185.55013
& - "[15] A bordism approach to string topology", Int. Math. Res. Not. 2005 (2005), p. 2829-2875. | Article | MR 2180465 | Zbl 1086.55004
- "[16] String topology of classifying spaces", preprint arXiv:AT/0801.0174. | Article | MR 2980450 | Zbl 1253.55008
& - "[17] A new cohomology theory of orbifold", Comm. Math. Phys. 248 (2004), p. 1-31. | Article | MR 2104605 | Zbl 1063.53091
& - "[18] The quantum orbifold cohomology of weighted projective spaces", Acta Math. 202 (2009), p. 139-193. | Article | MR 2506749 | Zbl 1213.53106
, , & - "[19] The Floer homotopy type of the cotangent bundle", preprint arXivrAT/0702852. | MR 2761853 | Zbl 1226.53086
- "[20] A polarized view of string topology", in Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., vol. 308, Cambridge Univ. Press, 2004, p. 127-154. | Article | MR 2079373 | Zbl 1095.55006
& - "[21] A homotopy theoretic realization of string topology", Math. Ann. 324 (2002), p. 773-798. | Article | MR 1942249 | Zbl 1025.55005
& - "[22] The loop homology algebra of spheres and projective spaces", in Categorical decomposition techniques in algebraic topology (Isle of Skye, 2001), Progr. Math., vol. 215, Birkhäuser, 2004, p. 77-92. | MR 2039760 | Zbl 1054.55006
, & - "[23] Notes on string topology", in String topology and cyclic homology, Adv. Courses Math. CRM Barcelona, Birkhäuser, 2006, p. 1-95. | MR 2240287
& - "[24] Topological conformal field theories and Calabi-Yau categories", Adv. Math. 210 (2007), p. 165-214. | MR 2298823 | Zbl 1171.14038
- "[25] Topological conformal field theories and gauge theories", Geom. Topol. 11 (2007), p. 1539-1579. | Article | MR 2326951 | Zbl 1139.32006
, "[26] Topological gauge theories and group cohomology", Comm. Math. Phys. 129 (1990), p. 393-429. | Article | MR 1048699 | Zbl 0703.58011
& - "[27] Orbifold cohomology for global quotients", Duke Math. J. 117 (2003), p. 197-227. | Article | MR 1971293 | Zbl 1086.14046
& - "[28] Rational string topology", J. Eur. Math. Soc. (JEMS) 9 (2007), p. 123-156. | EuDML 277192 | MR 2283106 | Zbl 1200.55015
, & - "[29] Twisted equivariant -theory with complex coefficients", J. Topol. 1 (2008), p. 16-44. | Article | MR 2365650 | Zbl 1188.19005
, & - "[30] Categorical framework for the study of singular spaces", Mem. Amer. Math. Soc. 31 (1981). | MR 609831 | Zbl 0467.55005
& - "[31] Batalin-Vilkovisky algebras and two-dimensional topological field theories", Comm. Math. Phys. 159 (1994), p. 265-285. | Article | MR 1256989 | Zbl 0807.17026
- "[32] Higher string topology operations", preprint arXiv:0711.4859.
- "[33] Orbifold cohomology of hypertoric varieties", Internat. J. Math. 19 (2008), p. 927-956. | Article | MR 2446508 | Zbl 1160.53024
& - "[34] Orbifold cohomology of torus quotients", Duke Math. J. 139 (2007), p. 89-139. | Article | MR 2322677 | Zbl 1159.14029
, & - "[35] Chen-Ruan cohomology of cotangent orbifolds and Chas-Sullivan string topology", Math. Res. Lett. 14 (2007), p. 491-501. | Article | MR 2318652 | Zbl 1127.53073
, , , & - "[36] Generalized string topology operations", Proc. Lond. Math. Soc. 96 (2008), p. 78-106. | Article | MR 2392316 | Zbl 1143.57012
& - "[37] Supersymmetry and equivariant de Rham theory, Mathematics Past and Present, Springer, 1999. | MR 1689252 | Zbl 0934.55007
& -[38] On Kontsevich's Hochschild cohomology conjecture", Compos. Math. 142 (2006), p. 143-168. | Article | MR 2197407 | Zbl 1109.18001
, & - "[39] Higher Franz-Reidemeister torsion, AMS/IP Studies in Advanced Math., vol. 31, Amer. Math. Soc., 2002. | MR 1945530 | Zbl 1016.19001
-[40] Stringy -theory and the Chern character", Invent. Math. 168 (2007), p. 23-81. | Article | MR 2285746 | Zbl 1132.14047
, & - "[41] The orbifold cohomology ring of simplicial toric stack bundles", Illinois J. Math. 52 (2008), p. 493-514. | MR 2524648 | Zbl 1231.14002
- "[42] Rational maps and string topology", Geom. Topol. 10 (2006), p. 1579-1606. | Article | MR 2284046 | Zbl 1204.58006
& - "[43] Sheaves on manifolds, Grund. Math. Wiss., vol. 292, Springer, 1990. | MR 1074006 | Zbl 0709.18001
& -[44] Opérations sur l'homologie cyclique des algèbres commutatives", Invent Math. 96 (1989), p. 205-230. | Article | EuDML 143678 | MR 981743 | Zbl 0686.18006
- "[45] Loop groupoids, gerbes, and twisted sectors on orbifolds", in Orbifolds in mathematics and physics (Madison, WI, 2001), Contemp. Math., vol. 310, Amer. Math. Soc., 2002, p. 163-184. | Article | MR 1950946 | Zbl 1041.58008
& - "[46] The loop orbifold of the symmetric product", J. Pure Appl. Algebra 211 (2007), p. 293-306. | Article | MR 2340450 | Zbl 1148.55005
, & - "[47] Orbifold string topology", Geom. Topol. 12 (2008), p. 2203-2247. | Article | MR 2431019 | Zbl 1149.55005
, & , "[48] Operads in algebra, topology and physics, Mathematical Surveys and Monographs, vol. 96, Amer. Math. Soc., 2002. | MR 1898414 | Zbl 1017.18001
, & -[49] Equivariant cohomology and the Cartan model", in Encyclopedia of Mathematical Physics, Elsevier, 2006. | Article
- "[50] Lie groupoids, sheaves and cohomology", in Poisson geometry, deformation quantisation and group representations, London Math. Soc. Lecture Note Ser., vol. 323, Cambridge Univ. Press, 2005, p. 145-272. | MR 2166453 | Zbl 1082.58018
& - "[51] Mapping stacks of topological stacks", J. reine angew. Math. 646 (2010), p. 117-133. | MR 2719557 | Zbl 1237.57027
- "[52] Foundations of topological stacks, I", preprint https://arxiv.org/abs/math/0503247.
, "[53] Homotopy types of topological stacks", preprint arXiv:0808.3799. | MR 2927363 | Zbl 1264.55010
, "[54] Framed discs operads and Batalin-Vilkovisky algebras", Q. J. Math. 54 (2003), p. 213-231. | Article | MR 1989873 | Zbl 1072.55006
& - "[55] Two-dimensional conformal field theories and modular functors", in IXth International Congress on Mathematical Physics (Swansea, 1988), Hilger, 1989, p. 22-37. | MR 1033753
- "[56] The definition of conformai field theory", in Topology, geometry and quantum field theory, London Math. Soc. Lecture Note Ser., vol. 308, Cambridge Univ. Press, 2004, p. 421-577. | MR 2079383 | Zbl 1372.81138
, "[57] Note on cofibrations", Math. Scand. 19 (1966), p. 11-14. | Article | EuDML 165952 | MR 211403 | Zbl 0145.43604
- "[58] Note on cofibrations. II", Math. Scand. 22 (1968), p. 130-142. | Article | EuDML 166037 | MR 243525 | Zbl 0181.26504
, "[59] String topology: Background and present state", preprint arXiv:AT/0710.4141. | Article | MR 2459297 | Zbl 1171.55003
- "[60] A homotopy theoretic proof of the BV identity in loop homology", preprint arXiv:AT/0706.1277.
- "[61] On the homotopy of the stable mapping class group", Invent. Math. 130 (1997), p. 257-275. | Article | MR 1474157 | Zbl 0891.55019
- "[62] Notes on universal algebra", in Graphs and patterns in mathematics and theoretical physics, Proc. Sympos. Pure Math., vol. 73, Amer. Math. Soc., 2005, p. 81-103. | Article | MR 2131012 | Zbl 1083.18005
- "[63] Elements of homotopy theory, Graduate Texts in Math., vol. 61, Springer, 1978. | Article | MR 516508 | Zbl 0406.55001
-[64] -groupoids and stacky groupoids", Int. Math. Res. Not. 2009 (2009), p. 4087-4141. | MR 2549951 | Zbl 1180.22006
-"