publication . Preprint . 2013

Holomorphic curves in exploded manifolds: Kuranishi structure

Parker, Brett;
Open Access English
  • Published: 20 Jan 2013
This paper constructs a Kuranishi structure for the moduli stack of holomorphic curves in exploded manifolds. To avoid some technicalities of abstract Kuranishi structures, we embed our Kuranishi structure inside a moduli stack of curves. The construction also works for the moduli stack of holomorphic curves in any compact symplectic manifold.
arXiv: Mathematics::Symplectic GeometryMathematics::Algebraic GeometryMathematics::Complex VariablesMathematics::Differential Geometry
free text keywords: Mathematics - Symplectic Geometry
Download from
16 references, page 1 of 2

[1] P. Deligne and D. Mumford. The irreducibility of the space of curves of given genus. Inst. Hautes E´tudes Sci. Publ. Math., (36):75-109, 1969. [OpenAIRE]

[2] Kenji Fuakay, Yong-Geun Oh, Hiroshi Ohta, and Kaoru Ono. Technical details on kuranishi structure and virtual fundamental chain. arXiv:12094410.

[3] Kenji Fukaya and Kaoru Ono. Arnold conjecture and Gromov-Witten invariant. Topology, 38(5):933-1048, 1999.

[4] Kenji Fukaya and Kaoru Ono. Floer homology and Gromov-Witten invariant over integer of general symplectic manifolds-summary. In Taniguchi Conference on Mathematics Nara '98, volume 31 of Adv. Stud. Pure Math., pages 75-91. Math. Soc. Japan, Tokyo, 2001. [OpenAIRE]

[5] H. Hofer, K. Wysocki, and E. Zehnder. A general Fredholm theory. I. A splicing-based differential geometry. J. Eur. Math. Soc. (JEMS), 9(4):841-876, 2007.

[6] Dominic Joyce. D-manifolds and d-orbifolds: a theory of derived diferential geometry. Unfinished book available here: joyce/dmanifolds.html.

[7] Dominic Joyce. Kuranishi bordism and kuranishi homology. math.SG/0707.3572v4, 2008.

[8] Finn F. Knudsen. The projectivity of the moduli space of stable curves. II. The stacks Mg,n. Math. Scand., 52(2):161-199, 1983.

[9] Eugene Lerman. Orbifolds as stacks? Enseign. Math. (2), 56(3-4):315-363, 2010.

[10] Dusa McDuff and Katrin Wehrheim. Smooth kuranishi structures with trivial isotropy. arXiv:1208.1340.

[11] Brett Parker. Holomorphic curves in exploded manifolds: compactness. arXiv:0911.2241, 2009.

[12] Brett Parker. De Rham theory of exploded manifolds. arXiv:1003.1977, 2011.

[13] Brett Parker. Holomorphic curves in exploded manifolds: Regularity. arXiv:0902.0087v2, 2011.

[14] Brett Parker. Exploded manifolds. Adv. Math., 229:3256-3319, 2012. arXiv:0910.4201.

[15] Brett Parker. Universal tropical structures for curves in exploded manifolds. arXiv, 2013.

16 references, page 1 of 2
Any information missing or wrong?Report an Issue