All Questions

Let $X$ be a finite CW-complex of dimension two having just one 0-cell (+ finitely many 1-cells + finitely many 2-cells). Is it true that X can be embedded in $\Bbb R^4$? If true, is it due to ...

Let $\mathcal K_7^2$ be the complete 2-dimensional simplicial complex on seven vertices, i.e. it has all $7\choose 2$ edges and all $7\choose 3$ 2-simplices (and no higher-dimensional simplices). I ...