3 problems

Direct-definition conjecture. The eta-type invariant defined using a cutoff function satisfies

Let $X$ be an even-dimensional manifold, let $E$ be the relevant flat Hermitian vector bundle with associated Dirac operator, let $g$ be the unitary automorphism used to define the…

Properness conjecture. For every such $P$ and $T$, the algebra $\mathcal{A}_{P_T}$ is different from