Mathematical Research Letters

Volume 22 (2015)

Number 4

Loop-fusion cohomology and transgression

Pages: 1177 – 1192



Chris Kottke (Department of Mathematics, Northeastern University, Boston, Massachusetts, U.S.A.)

Richard B. Melrose (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Mass., U.S.A.)


‘Loop-fusion cohomology’ is defined on the continuous loop space of a manifold in terms of Čech cochains satisfying two multiplicative conditions with respect to the fusion and figure-of-eight products on loops. The main result is that these cohomology groups, with coefficients in an abelian group, are isomorphic to those of the manifold and the transgression homomorphism factors through the isomorphism.

Accepted 6 May 2015

Published 24 July 2015