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8 votes
1 answer
224 views

Can increasing the winding number of a 2-cell make a CW complex embeddable?

Let $X$ be a 2-dimensional CW complex and let $c\subset X$ be a 2-cell attached along a simple closed loop $\gamma$ in the 1-skeleton $X^{(1)}$. For a natural number $n\ge 2$ consider the operation of ...
16 votes
3 answers
2k views

When does a CW-complex of dimension 2 embed in $\Bbb R^4$?

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 ...