Geometry & Topology Volume 19, issue 4 (2015)

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1364-0380

ISSN (print): 1465-3060

Author Index

To Appear

Other MSP Journals

The topology of the space of $J$–holomorphic maps to $\mathbb{C}\mathrm{P}^2$

Jeremy Miller

Geometry & Topology 19 (2015) 1829–1894

DOI: 10.2140/gt.2015.19.1829

Bibliography

1	M Abreu, Topology of symplectomorphism groups of $S^2\times S^2$, Invent. Math. 131 (1998) 1 MR1489893
2	R Andrade, From manifolds to invariants of En-algebras, PhD thesis, MIT (2010)
3	M F Atiyah, J D S Jones, Topological aspects of Yang–Mills theory, Comm. Math. Phys. 61 (1978) 97 MR503187
4	C P Boyer, K Galicki, Sasakian geometry, Oxford Univ. Press (2008) MR2382957
5	C P Boyer, B M Mann, Monopoles, nonlinear $\sigma$ models, and two-fold loop spaces, Comm. Math. Phys. 115 (1988) 571 MR933456
6	R L Cohen, J D S Jones, G B Segal, Stability for holomorphic spheres and Morse theory, from: "Geometry and topology" (editors K Grove, I H Madsen, E K Pedersen), Contemp. Math. 258, Amer. Math. Soc. (2000) 87 MR1778098
7	J Francis, The tangent complex and Hochschild cohomology of $\mathcal{E}_n$–rings, Compos. Math. 149 (2013) 430 MR3040746
8	K Fukaya, K Ono, Arnold conjecture and Gromov–Witten invariant for general symplectic manifolds, from: "The Arnoldfest" (editors E Bierstone, B Khesin, A Khovanskii, J E Marsden), Fields Inst. Commun. 24, Amer. Math. Soc. (1999) 173 MR1733575
9	M Gromov, Pseudoholomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
10	M A Guest, The topology of the space of rational curves on a toric variety, Acta Math. 174 (1995) 119 MR1310847
11	H Hofer, V Lizan, J C Sikorav, On genericity for holomorphic curves in four-dimensional almost-complex manifolds, J. Geom. Anal. 7 (1997) 149 MR1630789
12	S Ivashkovich, V Shevchishin, Structure of the moduli space in a neighborhood of a cusp-curve and meromorphic hulls, Invent. Math. 136 (1999) 571 MR1695206
13	S Kallel, Configuration spaces and the topology of curves in projective space, from: "Topology, geometry and algebra: Interactions and new directions" (editors A Adem, G Carlsson, R Cohen), Contemp. Math. 279, Amer. Math. Soc. (2001) 151 MR1850746
14	S Kallel, Spaces of particles on manifolds and generalized Poincaré dualities, Q. J. Math. 52 (2001) 45 MR1820902
15	S Kallel, I Saihi, Homotopy groups of diagonal complements, arXiv:1306.6272
16	B Kleiner, J Lott, Geometrization of three-dimensional orbifolds via Ricci flow, Astérisque 365, Soc. Math. France (2014) 101 MR3244330
17	J Li, G Tian, Virtual moduli cycles and Gromov–Witten invariants of algebraic varieties, J. Amer. Math. Soc. 11 (1998) 119 MR1467172
18	J Lurie, Derived algebraic geometry, VI: $E[k]$–algebras, online manuscript, (2009)
19	J P May, The geometry of iterated loop spaces, Lectures Notes in Math. 271, Springer (1972) MR0420610
20	D McDuff, Configuration spaces of positive and negative particles, Topology 14 (1975) 91 MR0358766
21	D McDuff, The local behaviour of holomorphic curves in almost complex $4$–manifolds, J. Differential Geom. 34 (1991) 143 MR1114456
22	D McDuff, D Salamon, $J$–holomorphic curves and quantum cohomology, Univ. Lecture Series 6, Amer. Math. Soc. (1994) MR1286255
23	J Miller, Homological stability properties of spaces of rational $J$–holomorphic curves in $\mathbb{P}^2$, Algebr. Geom. Topol. 13 (2013) 453 MR3031648
24	J Miller, Nonabelian Poincaré duality after stabilizing, Trans. Amer. Math. Soc. 367 (2015) 1969 MR3286505
25	Y Ruan, G Tian, A mathematical theory of quantum cohomology, J. Differential Geom. 42 (1995) 259 MR1366548
26	Y Ruan, G Tian, Higher genus symplectic invariants and sigma models coupled with gravity, Invent. Math. 130 (1997) 455 MR1483992
27	P Salvatore, Configuration spaces with summable labels, from: "Cohomological methods in homotopy theory" (editors J Aguadé, C Broto, C Casacuberta), Progr. Math. 196, Birkhäuser (2001) 375 MR1851264
28	Y Savelyev, On configuration spaces of stable maps, arXiv:1104.5440
29	G Segal, Configuration-spaces and iterated loop-spaces, Invent. Math. 21 (1973) 213 MR0331377
30	G Segal, The topology of spaces of rational functions, Acta Math. 143 (1979) 39 MR533892
31	B Siebert, Symplectic Gromov–Witten invariants, from: "New trends in algebraic geometry" (editors K Hulek, F Catanese, C Peters, M Reid), London Math. Soc. Lecture Note Ser. 264, Cambridge Univ. Press (1999) 375 MR1714832
32	B Siebert, G Tian, On the holomorphicity of genus two Lefschetz fibrations, Ann. of Math. 161 (2005) 959 MR2153404
33	J C Sikorav, The gluing construction for normally generic $J$–holomorphic curves, from: "Symplectic and contact topology: Interactions and perspectives" (editors Y Eliashberg, B Khesin, F Lalonde), Fields Inst. Commun. 35, Amer. Math. Soc. (2003) 175 MR1969276
34	M Weiss, What does the classifying space of a category classify?, Homology Homotopy Appl. 7 (2005) 185 MR2175298
35	K Yamaguchi, Configuration space models for spaces of maps from a Riemann surface to complex projective space, Publ. Res. Inst. Math. Sci. 39 (2003) 535 MR2001186