5 problems

Let $M$ be a compact oriented smooth manifold with smooth boundary $\partial M$, let $E_0$ and $E_1$ be smooth complex Hermitian vector bundles over $M$, and let…

Let $Sp(n)$ be the compact symplectic group, let $U(i)$ be the unitary group, and let $K.\Omega Sp(n)$ denote the K-homology ring of its based loop space. For $1\leq i\leq n$, the…

Uniform geometric K-homology conjecture. The natural map

Douglas's conjecture. Conjecture A holds true, and its induced extension class $\tau_I$ is identified with the fundamental class of $X_I$, namely the extension class induced by the…

Let $SG$ denote the Sierpiński gasket and let $(A,H,D)$ be a spectral triple for $C(SG)$ inducing the geodesic distance on the gasket. Suppose that it is summable for every…