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Ryan Budney
Ryan Budney
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There's an obstruction to embedding $n$-complexes in $\mathbb R^{2n}$ provided $n \geq 3$ due to Shapiro.

MR0089410 (19,671a) Shapiro, Arnold Obstructions to the imbedding of a complex in a euclidean space. I. The first obstruction. Ann. of Math. (2) 66 (1957), 256–269.

or as Ian suggests, van Kampen pre-dates Shapiro.

JFM 58.0615.03 van Kampen, E. R. Berichtung zu:``Komplexe in euklidischen Räumen''. (German) Abhandlungen Hamburg 9, 152-153 (1932).

Could you be more precise on how you want to modify the your complexes that originally are in $\mathbb R^3$, your special case?

There's an obstruction to embedding $n$-complexes in $\mathbb R^{2n}$ provided $n \geq 3$ due to Shapiro.

MR0089410 (19,671a) Shapiro, Arnold Obstructions to the imbedding of a complex in a euclidean space. I. The first obstruction. Ann. of Math. (2) 66 (1957), 256–269.

Could you be more precise on how you want to modify the your complexes that originally are in $\mathbb R^3$, your special case?

There's an obstruction to embedding $n$-complexes in $\mathbb R^{2n}$ provided $n \geq 3$ due to Shapiro.

MR0089410 (19,671a) Shapiro, Arnold Obstructions to the imbedding of a complex in a euclidean space. I. The first obstruction. Ann. of Math. (2) 66 (1957), 256–269.

or as Ian suggests, van Kampen pre-dates Shapiro.

JFM 58.0615.03 van Kampen, E. R. Berichtung zu:``Komplexe in euklidischen Räumen''. (German) Abhandlungen Hamburg 9, 152-153 (1932).

Could you be more precise on how you want to modify the your complexes that originally are in $\mathbb R^3$, your special case?

Source Link
Ryan Budney
Ryan Budney
  • 44.4k
  • 2
  • 139
  • 245

There's an obstruction to embedding $n$-complexes in $\mathbb R^{2n}$ provided $n \geq 3$ due to Shapiro.

MR0089410 (19,671a) Shapiro, Arnold Obstructions to the imbedding of a complex in a euclidean space. I. The first obstruction. Ann. of Math. (2) 66 (1957), 256–269.

Could you be more precise on how you want to modify the your complexes that originally are in $\mathbb R^3$, your special case?