English

The tangent bundle of an almost-complex free loopspace

Differential Geometry 2007-05-23 v2 Algebraic Topology

Abstract

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 \S 3.1 will fail in general to have constant rank, so the family TV{\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}

Keywords

Cite

@article{arxiv.math/0109085,
  title  = {The tangent bundle of an almost-complex free loopspace},
  author = {Jack Morava},
  journal= {arXiv preprint arXiv:math/0109085},
  year   = {2007}
}

Comments

This paper appears in the Proceedings of the Stanford Workshop on equivariant homotopy theory, published in Homology, Homotopy, and Applications 3 (2001) 407-415