The free loop space equivariant cohomology algebra of some formal spaces

摘要

Let mathbbK{mathbb{K}} be a field of characteristic p > 0 and S 1 the unit circle. We construct a model for the negative cylic homology of a commutative cochain algebra with two stages Sullivan minimal model. Using the notion of shc-formality introduced in Bitjong and Thomas (Topology 41:85–106), the main result of Bitjong and El Haouari (Math Ann 338:347–354) and techniques of Vigué-Poirrier (J Pure Appl Algebra 91:347–354) we compute the S 1-equivariant cohomology algebras of the free loop spaces of the infinite complex projective space mathbbCP(¥){mathbb{CP}(infty)} and the odd spheres S 2q+1.