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Ryan Grady and Owen Gwilliam
L∞ spaces and derived loop spaces view print
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| Published: |
April 21, 2015 |
| Keywords: |
derived geometry, deformation theory, higher Lie theory |
| Subject: |
14D23; 13D10, 18G55, 17B55 |
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Abstract
We develop further the approach to derived differential geometry introduced in Costello's work on the Witten genus (arXiv, 2011). In particular, we introduce several new examples of L∞ spaces, discuss vector bundles and shifted symplectic structures on L∞ spaces, and examine in some detail the example of derived loop spaces. This paper is background for a forthcoming paper in which we define a quantum field theory on a derived stack, building upon Costello's definition of an effective field theory (AMS Monographs, 2011).
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| Acknowledgements
The first author was partially supported by the National Science Foundation under Award DMS-1309118.
The second author was supported as a postdoctoral fellow by the National Science Foundation under Award DMS-1204826.
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| Author information
Ryan Grady:
Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston MA 02215, USA
regrady@math.bu.edu
Owen Gwilliam:
Max Planck Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
gwilliam@mpim-bonn.mpg.de
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