Mathematical Research Letters

Volume 22 (2015)

Number 2

The action on cohomology by compositions of rational maps

Pages: 605 – 632



Roland K. W. Roeder (Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, In., U.S.A.)


We use intuitive results from algebraic topology and intersection theory to clarify the pullback action on cohomology by compositions of rational maps. We use these techniques to prove a simple sufficient criterion for functoriality of a composition of two rational maps on all degrees of cohomology and we then reprove the criteria of Diller-Favre, Bedford-Kim, and Dinh-Sibony. We conclude with a cautionary example.


pullback on cohomology, dynamical degrees

2010 Mathematics Subject Classification

Primary 37F99. Secondary 32H50.

Published 16 April 2015