The tangent bundle of an almost-complex free loopspace

Original · EN

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 TV 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 math.AT/0303003 R. Cohen, A. Stacey, Fourier decomposition of loop bundles, available at math.AT/0210351