New York Journal of Mathematics
Volume 21 (2015) 231-272


Ryan Grady and Owen Gwilliam

L spaces and derived loop spaces

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Published: April 21, 2015
Keywords: derived geometry, deformation theory, higher Lie theory
Subject: 14D23; 13D10, 18G55, 17B55

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).


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.

Author information

Ryan Grady:
Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston MA 02215, USA

Owen Gwilliam:
Max Planck Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany