Geometry & Topology Volume 23, issue 4 (2019)

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Holomorphic curves in exploded manifolds: regularity

Brett Parker

Geometry & Topology 23 (2019) 1621–1690

DOI: 10.2140/gt.2019.23.1621

Bibliography

1	D Abramovich, Q Chen, Stable logarithmic maps to Deligne–Faltings pairs, II, Asian J. Math. 18 (2014) 465 MR3257836
2	B Chen, A M Li, B L Wang, Virtual neighborhood technique for pseudo-holomorphic spheres, preprint (2013) arXiv:1306.3276
3	Q Chen, Stable logarithmic maps to Deligne–Faltings pairs, I, Ann. of Math. 180 (2014) 455 MR3224717
4	K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant, Topology 38 (1999) 933 MR1688434
5	M Gross, B Siebert, Logarithmic Gromov–Witten invariants, J. Amer. Math. Soc. 26 (2013) 451 MR3011419
6	H Hofer, A general Fredholm theory and applications, from: "Current developments in mathematics, 2004" (editors D Jerison, B Mazur, T Mrowka, W Schmid, R Stanley, S T Yau), International (2006) 1 MR2459290
7	H Hofer, K Wysocki, E Zehnder, A general Fredholm theory, I : A splicing-based differential geometry, J. Eur. Math. Soc. 9 (2007) 841 MR2341834
8	H Hofer, K Wysocki, E Zehnder, A general Fredholm theory, II : Implicit function theorems, Geom. Funct. Anal. 19 (2009) 206 MR2507223
9	H Hofer, K Wysocki, E Zehnder, A general Fredholm theory, III : Fredholm functors and polyfolds, Geom. Topol. 13 (2009) 2279 MR2515707
10	H Hofer, K Wysocki, E Zehnder, Integration theory on the zero sets of polyfold Fredholm sections, Math. Ann. 346 (2010) 139 MR2558891
11	H Hofer, K Wysocki, E Zehnder, Sc-smoothness, retractions and new models for smooth spaces, Discrete Contin. Dyn. Syst. 28 (2010) 665 MR2644764
12	E N Ionel, GW invariants relative to normal crossing divisors, Adv. Math. 281 (2015) 40 MR3366837
13	J Li, G Tian, Virtual moduli cycles and Gromov–Witten invariants of general symplectic manifolds, from: "Topics in symplectic 4–manifolds" (editor R J Stern), First Int. Press Lect. Ser. 1, International (1998) 47 MR1635695
14	G Liu, G Tian, Floer homology and Arnold conjecture, J. Differential Geom. 49 (1998) 1 MR1642105
15	R B Lockhart, R C McOwen, Elliptic differential operators on noncompact manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 12 (1985) 409 MR837256
16	D McDuff, The virtual moduli cycle, from: "Northern California Symplectic Geometry Seminar" (editors Y Eliashberg, D Fuchs, T Ratiu, A Weinstein), Amer. Math. Soc. Transl. Ser. 2 196, Amer. Math. Soc. (1999) 73 MR1736215
17	D McDuff, D Salamon, J–holomorphic curves and symplectic topology, 52, Amer. Math. Soc. (2004) MR2045629
18	B Parker, Exploded manifolds, Adv. Math. 229 (2012) 3256 MR2900440
19	B Parker, Log geometry and exploded manifolds, Abh. Math. Semin. Univ. Hambg. 82 (2012) 43 MR2922725
20	B Parker, Holomorphic curves in exploded manifolds: Kuranishi structure, preprint (2013) arXiv:1301.4748
21	B Parker, Universal tropical structures for curves in exploded manifolds, preprint (2013) arXiv:1301.4745
22	B Parker, On the value of thinking tropically to understand Ionel’s GW invariants relative normal crossing divisors, preprint (2014) arXiv:1407.3020
23	B Parker, Tropical enumeration of curves in blowups of the projective plane, preprint (2014) arXiv:1411.5722
24	B Parker, Gluing formula for Gromov–Witten invariants in a triple product, preprint (2015) arXiv:1511.0779
25	B Parker, Holomorphic curves in exploded manifolds: compactness, Adv. Math. 283 (2015) 377 MR3383807
26	B Parker, Notes on exploded manifolds and a tropical gluing formula for Gromov–Witten invariants, preprint (2016) arXiv:1605.00577
27	B Parker, Three dimensional tropical correspondence formula, Comm. Math. Phys. 353 (2017) 791 MR3649486
28	B Parker, Tropical gluing formulae for Gromov–Witten invariants, preprint (2017) arXiv:1703.05433
29	B Parker, De Rham theory of exploded manifolds, Geom. Topol. 22 (2018) 1
30	B Parker, Holomorphic curves in exploded manifolds: virtual fundamental class, Geom. Topol. 23 (2019) 1877
31	Y Ruan, Virtual neighborhoods and pseudo-holomorphic curves, Turkish J. Math. 23 (1999) 161 MR1701645