K-theory of the algebra A(M) associated to Hilbert–Hadamard spaces

Determine the K-theory of the C*-algebra A(M) associated to an admissible Hilbert–Hadamard space M, in general and without additional simplifying assumptions, so as to enable cutting-and-pasting approaches without recourse to deformation arguments.

Background

A central technical obstacle identified by the authors is the difficulty of computing the K-theory of the coefficient algebra A(M) tied to Hilbert–Hadamard spaces. This limitation motivates their development of deformation techniques and localization-algebra methods to bypass direct computation.

Clarifying the K-theory of A(M) would significantly strengthen and simplify arguments in the equivariant coarse setting and could advance understanding of Novikov-type conjectures for actions on nonpositively curved infinite-dimensional spaces.