Homology, Homotopy and Applications, vol.5(1), 2003, pp.71–71

ERRATUM TO ”THE TANGENT BUNDLE OF AN ALMOST

COMPLEX FREE LOOPSPACE” [HHA, V. 3(2)(2001), 407–415]

JACK MORAVA

(communicated by Hvedri Inassaridze)

The main construction of this paper contains a serious (fatal) error; I withdraw the claims made there.

I owe Andrew Stacey and Ralph Cohen thanks for seeing this; in particular, Stacey [1] has shown that the projections constructed in §3.1 of my paper 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 created this confusion. To researchers interested in these questions, I recommend the papers of Cohen, Godin, and Stacey cited below.

References

[1] A. Stacey, Properties of Morton’s logarithm, private communication [9 April 2002]

[2] R. Cohen, V. Godin, A polarized view of string topology, available at

     math.AT/0303003

[3] R. Cohen, A. Stacey, Fourier decomposition of loop bundles, available at

     math.AT/0210351

This article may be accessed via WWW at http://www.rmi.acnet.ge/hha/ or by anonymous ftp at

ftp://ftp.rmi.acnet.ge/pub/hha/volumes/2003/n1a4/v5n1a4.(dvi,ps,pdf)

Jack Morava jack@math.jhu.edu

Department of Mathematics Johns Hopkins University Baltimore, Maryland 21218

Received April 7, 2003; published on April 14, 2003.

\begin{matrix}c \\ ◯ \end{matrix} 2003, Jack Morava. Permission to copy for private use granted.