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Brane actions, categorifications of Gromov–Witten theory and quantum K–theory

Etienne Mann and Marco Robalo

Geometry & Topology 22 (2018) 1759–1836
Bibliography
1 C Barwick, On the Q construction for exact quasicategories, preprint (2013) arXiv:1301.4725
2 K Behrend, Gromov–Witten invariants in algebraic geometry, Invent. Math. 127 (1997) 601 MR1431140
3 K Behrend, B Fantechi, The intrinsic normal cone, Invent. Math. 128 (1997) 45 MR1437495
4 K Behrend, Y Manin, Stacks of stable maps and Gromov–Witten invariants, Duke Math. J. 85 (1996) 1 MR1412436
5 D Ben-Zvi, J Francis, D Nadler, Integral transforms and Drinfeld centers in derived algebraic geometry, J. Amer. Math. Soc. 23 (2010) 909 MR2669705
6 B Bhatt, Algebraization and Tannaka duality, Camb. J. Math. 4 (2016) 403 MR3572635
7 B Bhatt, D Halpern-Leistner, Tannaka duality revisited, Adv. Math. 316 (2017) 576 MR3672914
8 A Brini, R Cavalieri, Crepant resolutions and open strings, II, preprint (2014) arXiv:1407.2571
9 A Brini, R Cavalieri, D Ross, Crepant resolutions and open strings, preprint (2013) arXiv:1309.4438
10 J Bryan, T Graber, The crepant resolution conjecture, from: "Algebraic geometry, I" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 23 MR2483931
11 A Chiodo, H Iritani, Y Ruan, Landau–Ginzburg/Calabi–Yau correspondence, global mirror symmetry and Orlov equivalence, Publ. Math. Inst. Hautes Études Sci. 119 (2014) 127 MR3210178
12 H Chu, R Haugseng, G Heuts, Two models for the homotopy theory of –operads, preprint (2016) arXiv:1606.03826
13 I Ciocan-Fontanine, M Kapranov, Virtual fundamental classes via dg–manifolds, Geom. Topol. 13 (2009) 1779 MR2496057
14 D C Cisinski, Les préfaisceaux comme modèles des types d’homotopie, 308, Soc. Math. France (2006) MR2294028
15 D C Cisinski, I Moerdijk, Dendroidal sets as models for homotopy operads, J. Topol. 4 (2011) 257 MR2805991
16 D C Cisinski, I Moerdijk, Dendroidal Segal spaces and –operads, J. Topol. 6 (2013) 675 MR3100887
17 D C Cisinski, I Moerdijk, Dendroidal sets and simplicial operads, J. Topol. 6 (2013) 705 MR3100888
18 T Coates, A Corti, H Iritani, H H Tseng, Computing genus-zero twisted Gromov–Witten invariants, Duke Math. J. 147 (2009) 377 MR2510741
19 T Coates, A Givental, Quantum Riemann–Roch, Lefschetz and Serre, Ann. of Math. 165 (2007) 15 MR2276766
20 T Coates, H Iritani, Y Jiang, The crepant transformation conjecture for toric complete intersections, preprint (2014) arXiv:1410.0024
21 T Coates, H Iritani, H H Tseng, Wall-crossings in toric Gromov–Witten theory, I : Crepant examples, Geom. Topol. 13 (2009) 2675 MR2529944
22 K Costello, Higher genus Gromov–Witten invariants as genus zero invariants of symmetric products, Ann. of Math. 164 (2006) 561 MR2247968
23 V Drinfeld, D Gaitsgory, On some finiteness questions for algebraic stacks, preprint (2011) arXiv:1108.5351
24 B Dubrovin, Geometry of 2D topological field theories, from: "Integrable systems and quantum groups" (editors M Francaviglia, S Greco), Lecture Notes in Math. 1620, Springer (1996) 120 MR1397274
25 D Dugger, S Hollander, D C Isaksen, Hypercovers and simplicial presheaves, Math. Proc. Cambridge Philos. Soc. 136 (2004) 9 MR2034012
26 T Dyckerhoff, M Kapranov, Higher Segal spaces, I, preprint (2012) arXiv:1212.3563
27 W Fulton, R Pandharipande, Notes on stable maps and quantum cohomology, from: "Algebraic geometry" (editors J Kollár, R Lazarsfeld, D R Morrison), Proc. Sympos. Pure Math. 62, Amer. Math. Soc. (1997) 45 MR1492534
28 D Gaitsgory, Sheaves of categories and the notion of 1–affineness, preprint (2013) arXiv:1306.4304
29 D Gaitsgory, N Rozenblyum, Ind-coherent sheaves, preprint (2012) arXiv:1105.4857
30 D Gaitsgory, N Rozenblyum, A study in derived algebraic geometry, book project (2016)
31 E Getzler, M M Kapranov, Modular operads, Compositio Math. 110 (1998) 65 MR1601666
32 A Givental, On the WDVV equation in quantum K–theory, Michigan Math. J. 48 (2000) 295 MR1786492
33 A B Givental, Symplectic geometry of Frobenius structures, from: "Frobenius manifolds" (editors C Hertling, M Marcolli), Aspects Math. E36, Vieweg (2004) 91 MR2115767
34 T Graber, R Pandharipande, Localization of virtual classes, Invent. Math. 135 (1999) 487 MR1666787
35 P Hackney, M Robertson, D Yau, Higher cyclic operads, preprint (2017) arXiv:1611.02591
36 J Hall, D Rydh, Perfect complexes on algebraic stacks, Compositio Math. 153 (2017) 2318
37 D Halpern-Leistner, A Preygel, Mapping stacks and categorical notions of properness, preprint (2014) arXiv:1402.3204
38 R Haugseng, Iterated spans and “classical” topological field theories, preprint (2017) arXiv:1409.0837
39 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
40 H Iritani, An integral structure in quantum cohomology and mirror symmetry for toric orbifolds, Adv. Math. 222 (2009) 1016 MR2553377
41 H Iritani, Ruan’s conjecture and integral structures in quantum cohomology, from: "New developments in algebraic geometry, integrable systems and mirror symmetry" (editors M H Saito, S Hosono, K Yoshioka), Adv. Stud. Pure Math. 59, Math. Soc. Japan (2010) 111 MR2683208
42 M Kapranov, Y Manin, Modules and Morita theorem for operads, Amer. J. Math. 123 (2001) 811 MR1854112
43 L Katzarkov, M Kontsevich, T Pantev, Hodge theoretic aspects of mirror symmetry, from: "From Hodge theory to integrability and TQFT tt–geometry" (editors R Y Donagi, K Wendland), Proc. Sympos. Pure Math. 78, Amer. Math. Soc. (2008) 87 MR2483750
44 F F Knudsen, The projectivity of the moduli space of stable curves, II : The stacks Mg,n, Math. Scand. 52 (1983) 161 MR702953
45 M Kontsevich, Enumeration of rational curves via torus actions, from: "The moduli space of curves" (editors R Dijkgraaf, C Faber, G van der Geer), Progr. Math. 129, Birkhäuser (1995) 335 MR1363062
46 M Kontsevich, Y Manin, Gromov–Witten classes, quantum cohomology, and enumerative geometry, Comm. Math. Phys. 164 (1994) 525 MR1291244
47 Y P Lee, Quantum K–theory, I : Foundations, Duke Math. J. 121 (2004) 389 MR2040281
48 J Li, A degeneration formula of GW–invariants, J. Differential Geom. 60 (2002) 199 MR1938113
49 P Lowrey, T Schürg, Grothendieck–Riemann–Roch for derived schemes, preprint (2012) arXiv:1208.6325
50 J Lurie, Higher topos theory, 170, Princeton Univ. Press (2009) MR2522659
51 J Lurie, Derived algebraic geometry, IX: Closed immersions, preprint (2011)
52 J Lurie, Derived algebraic geometry, V: Structured spaces, preprint (2011)
53 J Lurie, Derived algebraic geometry, XIV: Representability theorems, preprint (2012)
54 J Lurie, Higher algebra, book project (2016)
55 J Lurie, Spectral algebraic geometry, book project (2016)
56 Y. Manin, Quantum cohomology, motives, derived categories, I–II, lecture notes (2013)
57 I Moerdijk, I Weiss, Dendroidal sets, Algebr. Geom. Topol. 7 (2007) 1441 MR2366165
58 F Perroni, Chen–Ruan cohomology of ADE singularities, Internat. J. Math. 18 (2007) 1009 MR2360646
59 S D Raskin, Chiral principal series categories, PhD thesis, Harvard University (2014) MR3251357
60 M Robalo, Théorie homotopique motivique des espaces noncommutatifs, PhD thesis, Université de Montpellier (2014)
61 M Robalo, K–theory and the bridge from motives to noncommutative motives, Adv. Math. 269 (2015) 399 MR3281141
62 Y Ruan, Topological sigma model and Donaldson-type invariants in Gromov theory, Duke Math. J. 83 (1996) 461 MR1390655
63 Y Ruan, The cohomology ring of crepant resolutions of orbifolds, from: "Gromov–Witten theory of spin curves and orbifolds" (editors T J Jarvis, T Kimura, A Vaintrob), Contemp. Math. 403, Amer. Math. Soc. (2006) 117 MR2234886
64 Y Ruan, G Tian, A mathematical theory of quantum cohomology, Math. Res. Lett. 1 (1994) 269 MR1266766
65 Y Ruan, G Tian, Higher genus symplectic invariants and sigma models coupled with gravity, Invent. Math. 130 (1997) 455 MR1483992
66 T Schürg, Deriving Deligne–Mumford stacks with perfect obstruction theories, Geom. Topol. 17 (2013) 73 MR3035324
67 T Schürg, B Toën, G Vezzosi, Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes, J. Reine Angew. Math. 702 (2015) 1 MR3341464
68 B Toën, The homotopy theory of dg–categories and derived Morita theory, Invent. Math. 167 (2007) 615 MR2276263
69 B Toën, Higher and derived stacks: a global overview, from: "Algebraic geometry, I" (editors D Abramovich, A Bertram, L Katzarkov, R Pandharipande, M Thaddeus), Proc. Sympos. Pure Math. 80, Amer. Math. Soc. (2009) 435 MR2483943
70 B Toën, Derived Azumaya algebras and generators for twisted derived categories, Invent. Math. 189 (2012) 581 MR2957304
71 B Toën, Proper local complete intersection morphisms preserve perfect complexes, preprint (2012) arXiv:1210.2827
72 B Toën, Operations on derived moduli spaces of branes, preprint (2013) arXiv:1307.0405
73 B Toën, Derived algebraic geometry, EMS Surv. Math. Sci. 1 (2014) 153 MR3285853
74 B Toën, G Vezzosi, Homotopical algebraic geometry, II : Geometric stacks and applications, 902, Amer. Math. Soc. (2008) MR2394633
75 H H Tseng, Orbifold quantum Riemann–Roch, Lefschetz and Serre, Geom. Topol. 14 (2010) 1 MR2578300