We show vanishing of some cup products on the rational cohomology of the mapping space from the k-sphere to a Poincaré duality space. When k is odd, it can be proved by using the brane coproduct, which is a generalization of the loop coproduct. In this talk, we focus on the case that k is even. In that case, the key of the proof is a convenient algebraic model of the mapping space, which is constructed by using the notion of regular sequences (from commutative ring theory) and its relationship to Poincaré duality.

This is an online seminar. Please register at:

https://docs.google.com/forms/d/e/1FAIpQLSc70fpYIp7Gwx_0g9su-snbPThzhRn…