The tangent bundle of an almost-complex free loopspace
Abstract
Description
The main construction of this paper contains a serious error, and I am withdrawing it.
I owe Andrew Stacey and Ralph Cohen thanks for seeing the problem; in particular, Stacey has shown that the projections constructed in §3.1 will fail in general to have constant rank, so the family ${\bf T}V$ of vector spaces defined by their images fails to be a vector bundle.
I'm very sorry to have caused this confusion. To researchers interested in these questions, I recommend the papers of Cohen, Godin, and Stacey cited below:
R. Cohen, V. Godin, A polarized view of string topology, available at {\tt math.AT/0303003}
R. Cohen, A. Stacey, Fourier decomposition of loop bundles, available at {\tt math.AT/0210351}
This paper appears in the Proceedings of the Stanford Workshop on equivariant homotopy theory, published in Homology, Homotopy, and Applications 3 (2001) 407-415
This paper appears in the Proceedings of the Stanford Workshop on equivariant homotopy theory, published in Homology, Homotopy, and Applications 3 (2001) 407-415