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5 - An introduction to d-manifolds and derived differential geometry

Published online by Cambridge University Press:  05 April 2014

By
Dominic Joyce
Edited by
Leticia Brambila-Paz ,
Peter Newstead ,
Richard P. Thomas  and
Oscar García-Prada
Dominic Joyce
Affiliation:
University of Oxford
Leticia Brambila-Paz
Affiliation:
Centro de Investigación en Matemáticas A.C. (CIMAT), Mexico
Peter Newstead
Affiliation:
University of Liverpool
Richard P. Thomas
Affiliation:
Imperial College of Science, Technology and Medicine, London
Oscar García-Prada
Affiliation:
Consejo Superior de Investigaciones Cientificas, Madrid
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Chapter
Information
Moduli Spaces , pp. 230 - 281
Publisher: Cambridge University Press
Print publication year: 2014

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References

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[11] R., Hartshorne, Algebraic Geometry, Graduate Texts in Math. 52, Springer, New York, 1977.
[12] H., Hofer, K., Wysocki and E., Zehnder, A general Fredholm theory I: A splicing-based differential geometry, J. Eur. Math. Soc. 9 (2007), 841–876. math.FA/0612604.
[13] H., Hofer, K., Wysocki and E., Zehnder, Integration theory for zero sets of polyfold Fredholm sections, arXiv:0711.0781, 2007.
[14] H., Hofer, K., Wysocki and E., Zehnder, Applications of polyfold theory I: the polyfolds of Gromov–Witten theory, arXiv:1107.2097, 2011.
[15] D., Huybrechts and R.P., Thomas, Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes, Math. Ann. 346 (2010), 545–569. arXiv:0805.3527.
[16] D., Joyce, Kuranishi homology and Kuranishi cohomology: a User's Guide, math.SG/0710.5634, 2007.
[17] D., Joyce, On manifolds with corners, arXiv:0910.3518, 2009.
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[19] D., Joyce, An introduction to C∞-schemes and C∞-algebraic geometry, pages 299–325 in H.-D., Cao and S.-T., Yau, editors, In memory of C.C. Hsiung: Lectures given at the JDG symposium, Lehigh University, June 2010, Surveys in Differential Geometry 17, 2012. arXiv:1104.4951.
[20] D., Joyce, D-manifolds and d-orbifolds: a theory of derived differential geometry, book in preparation, 2012. Preliminary version available at http://people.maths.ox.ac.uk/~joyce/dmanifolds.html.
[21] D., Joyce, D-manifolds, d-orbifolds and derived differential geometry: a detailed summary, arXiv: 1208.4948, 2012.
[22] M., Kontsevich, Enumeration of rational curves via torus actions, pages 335–368 in R., Dijkgraaf, C., Faber and G., van der Geer, editors, The moduli space of curves, Progr. Math. 129, Birkhäuser, 1995. hep-th/9405035.
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[34] H., Whitney, Differentiable manifolds, Ann. Math. 37 (1936), 645–680.

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