Grothendieck duality theory assigns to essentially-finite-type maps f of noetherian schemes a pseudofunctor f× right-adjoint to Rf∗, and a pseudofunctor f ! agreeing with f× when f is proper, but equal to the usual inverse image f∗ when f is étale. We define and study a canonical map from the first pseudofunctor to the second. This map behaves well with respect to flat base change, and is taken...

Inspired by work of Lipshitz-Sarkar, we show that the module structure on link Floer homology detects split links. Using results Ni, Alishahi-Lipshitz, and establish an analogous detection result for sutured homology.

If H is a nitely generated subgroup of the nitely generated group G, then H is undistorted in G for their word metrics ii the induced homomorphism on the zero-dimensionaì 1-homology group is injective. The Mayer-Vietoris exact sequence for`1-homology is established and applications are given to hyperbolic groups and relative hyperbolicity. The notion of relative distortion of two maps is introd...