Mathematical Research Letters
Volume 22 (2015)
The action on cohomology by compositions of rational maps
Pages: 605 – 632
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.