3 problems

Let $p\colon M\to B$ be a smooth family of manifolds, and let $p_!$ denote the pushdown in Lott's real differential $K$-theory. Lott's conjecture. The $\Kqo_R$-pushdown is related…

Let $M$ be a closed $n$-dimensional $\operatorname{Pin}^{+}$ manifold, and let $E\to M$ be an orthogonal vector bundle with covariant derivative. Write…

Differential equivariant pushforward conjecture. The equality holds as class functions modulo $R(\Gamma)$. This conjectures that the index-theoretic description of the ordinary equ…