EQUIVARIANT CALCULUS OF FUNCTORS AND Z/2-ANALYTICITY OF REAL ALGEBRAIC K-THEORY

作者：Dotto Emanuele^*

来源：Journal of the Institute of Mathematics of Jussieu, 2016, 15(4): 829-883.

DOI：10.1017/S1474748015000067

• Hermitian K-theory
• equivariant homotopy theory

We define a theory of Goodwillie calculus for enriched functors from finite pointed simplicial G-sets to symmetric G-spectra, where G is a finite group. We extend a notion of G-linearity suggested by Blumberg to define stably excisive and rho-analytic homotopy functors, as well as a G-differential, in this equivariant context. A main result of the paper is that analytic functors with trivial derivatives send highly connected G-maps to G-equivalences. It is analogous to the classical result of Goodwillie that 'functors with zero derivative are locally constant'. As the main example, we show that Hesselholt and Madsen's Real algebraic K-theory of a split square zero extension of Wall antistructures defines an analytic functor in the Z/2-equivariant setting. We further show that the equivariant derivative of this Real K-theory functor is Z/2-equivalent to Real MacLane homology.

• 出版日期2016-10
• 单位MIT