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compacta has been changed to polyhedra
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M.Ramana
M.Ramana
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Homotopy domination of a wedge of two compactapolyhedra

The topological space $A$ is called homotopy dominated by the space $X$ if there are maps $f:A\longrightarrow X$ and $g:X\longrightarrow A$ so that $g\circ f\simeq id_A$.

Question: Suppose that $X_1$ and $X_2$ are two compactapolyhedra. If $A$ is homotopy dominated by $X_1\vee X_2$, then is $A$ of the form $A_1 \vee A_2$ (up to homotopy equivalent) where $A_i$ is homotopy dominated by $X_i$ for $i=1,2$?

Homotopy domination of a wedge of two compacta

The topological space $A$ is called homotopy dominated by the space $X$ if there are maps $f:A\longrightarrow X$ and $g:X\longrightarrow A$ so that $g\circ f\simeq id_A$.

Question: Suppose that $X_1$ and $X_2$ are two compacta. If $A$ is homotopy dominated by $X_1\vee X_2$, then is $A$ of the form $A_1 \vee A_2$ (up to homotopy equivalent) where $A_i$ is homotopy dominated by $X_i$ for $i=1,2$?

Homotopy domination of a wedge of two polyhedra

The topological space $A$ is called homotopy dominated by the space $X$ if there are maps $f:A\longrightarrow X$ and $g:X\longrightarrow A$ so that $g\circ f\simeq id_A$.

Question: Suppose that $X_1$ and $X_2$ are two polyhedra. If $A$ is homotopy dominated by $X_1\vee X_2$, then is $A$ of the form $A_1 \vee A_2$ (up to homotopy equivalent) where $A_i$ is homotopy dominated by $X_i$ for $i=1,2$?

added 60 characters in body; edited title
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M.Ramana
M.Ramana
  • 1.2k
  • 5
  • 11

Concerning Homotopy domination of a wedge of two spacescompacta

The topological space $A$ is called homotopy dominated by the space $X$ if there are maps $f:A\longrightarrow X$ and $g:X\longrightarrow A$ so that $g\circ f\simeq id_A$.

Question: IfSuppose that $X_1$ and $X_2$ are two compacta. If $A$ is homotopy dominated by $X_1\vee X_2$, then is $A$ of the form $A_1 \vee A_2$ (up to homotopy equivalent) where $A_i$ is homotopy dominated by $X_i$ for $i=1,2$?

Concerning domination of a wedge of two spaces

The space $A$ is called homotopy dominated by the space $X$ if there are maps $f:A\longrightarrow X$ and $g:X\longrightarrow A$ so that $g\circ f\simeq id_A$.

Question: If $A$ is homotopy dominated by $X_1\vee X_2$, then is $A$ of the form $A_1 \vee A_2$ (up to homotopy equivalent) where $A_i$ is homotopy dominated by $X_i$ for $i=1,2$?

Homotopy domination of a wedge of two compacta

The topological space $A$ is called homotopy dominated by the space $X$ if there are maps $f:A\longrightarrow X$ and $g:X\longrightarrow A$ so that $g\circ f\simeq id_A$.

Question: Suppose that $X_1$ and $X_2$ are two compacta. If $A$ is homotopy dominated by $X_1\vee X_2$, then is $A$ of the form $A_1 \vee A_2$ (up to homotopy equivalent) where $A_i$ is homotopy dominated by $X_i$ for $i=1,2$?

Source Link
M.Ramana
M.Ramana
  • 1.2k
  • 5
  • 11

Concerning domination of a wedge of two spaces

The space $A$ is called homotopy dominated by the space $X$ if there are maps $f:A\longrightarrow X$ and $g:X\longrightarrow A$ so that $g\circ f\simeq id_A$.

Question: If $A$ is homotopy dominated by $X_1\vee X_2$, then is $A$ of the form $A_1 \vee A_2$ (up to homotopy equivalent) where $A_i$ is homotopy dominated by $X_i$ for $i=1,2$?