Skip to main content
MathOverflow

Return to Question

formatting
Source Link
YCor
YCor
  • 63.9k
  • 5
  • 187
  • 286

Homotopy Groupsgroups of Quotientquotient of SU(n)

Let $X$ be the quotient topological space obtained by identifying the matrices $A$ and $\overline{A}$ in the topological group $\text{SU}(n)$$\mathrm{SU}(n)$ (here $\overline{A}$ denotes entry-wise complex conjugation). Are there any techniques for finding the second homotopy group of $X$? For example, is the quotient map $p:\text{SU}(n) \rightarrow X$$p:\mathrm{SU}(n) \rightarrow X$ a fibration?

Homotopy Groups of Quotient of SU(n)

Let $X$ be the quotient topological space obtained by identifying the matrices $A$ and $\overline{A}$ in the topological group $\text{SU}(n)$ (here $\overline{A}$ denotes entry-wise complex conjugation). Are there any techniques for finding the second homotopy group of $X$? For example, is the quotient map $p:\text{SU}(n) \rightarrow X$ a fibration?

Homotopy groups of quotient of SU(n)

Let $X$ be the quotient topological space obtained by identifying the matrices $A$ and $\overline{A}$ in the topological group $\mathrm{SU}(n)$ (here $\overline{A}$ denotes entry-wise complex conjugation). Are there any techniques for finding the second homotopy group of $X$? For example, is the quotient map $p:\mathrm{SU}(n) \rightarrow X$ a fibration?

Source Link
Quizzical
Quizzical
  • 271
  • 1
  • 5

Homotopy Groups of Quotient of SU(n)

Let $X$ be the quotient topological space obtained by identifying the matrices $A$ and $\overline{A}$ in the topological group $\text{SU}(n)$ (here $\overline{A}$ denotes entry-wise complex conjugation). Are there any techniques for finding the second homotopy group of $X$? For example, is the quotient map $p:\text{SU}(n) \rightarrow X$ a fibration?