Counterexamples to the simple loop conjecture in higher-dimension

Abstract

For every $g\ge 2$ and $n\ge 4$, we provide an $n-$manifold $M$ and a continuous $2-$sided map $f:S⟶M$, where $S$ is a closed genus $g$ surface, such that no simple loop is contained in $\text{ker}(f_{\ast })$. This provides a counterexample to the the classical simple loop conjecture for surfaces to manifolds of dimensions at least four.

6 pages, no figures