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LSpice
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Approximate classyfingclassifying space by boundaryless manifolds?

As pointed outpointed out by Achim Krause, any finite CW complex is homotopy equivalent to a manifold with boundary (by embedding into ℝ𝑛$\mathbb R^n$ and thickening), and so every finite type CW complex can be approximated by manifolds with boundary.

Given a Lie group $G$, is it possible to approximate $BG$ by using boundaryless manifolds? For example, $BS^1$ can be approximated by $\mathbb{CP}^N$. Is this a general phenomenon or special case for torus? (The classfyingclassifying space of a torus supports a group structure, so it has to be boundaryless.)

Approximate classyfing space by boundaryless manifolds?

As pointed out by Achim Krause, any finite CW complex is homotopy equivalent to a manifold with boundary (by embedding into ℝ𝑛 and thickening), and so every finite type CW complex can be approximated by manifolds with boundary.

Given a Lie group $G$, is it possible to approximate $BG$ by using boundaryless manifolds? For example, $BS^1$ can be approximated by $\mathbb{CP}^N$. Is this a general phenomenon or special case for torus? (The classfying space of torus supports a group structure, so it has to be boundaryless)

Approximate classifying space by boundaryless manifolds?

As pointed out by Achim Krause, any finite CW complex is homotopy equivalent to a manifold with boundary (by embedding into $\mathbb R^n$ and thickening), and so every finite type CW complex can be approximated by manifolds with boundary.

Given a Lie group $G$, is it possible to approximate $BG$ by using boundaryless manifolds? For example, $BS^1$ can be approximated by $\mathbb{CP}^N$. Is this a general phenomenon or special case for torus? (The classifying space of a torus supports a group structure, so it has to be boundaryless.)

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Is it possible the Approximate classyfing space is a manifold with boundaryby boundaryless manifolds?

As the classfying space $BG$ of a Lie group $G$pointed out by Achim Krause, is it possible itany finite CW complex is homotopy equivalent to a manifold with boundary? More generally (by embedding into ℝ𝑛 and thickening), ifand so every finite type CW complex can be approximated by manifolds with boundary.

Given a Lie group $BG$ is infinite dimensional$G$, is it possible it's approxiamtedto approximate $BG$ by using boundaryless manifolds with boundaries? For example, $BS^1$ can be approximated by $\mathbb{CP}^N$. Is this a general phenomenon or special case for torus? (The classfying space of torus supports a group structure, so it has to be boundaryless)

Is it possible the classyfing space is a manifold with boundary?

As the classfying space $BG$ of a Lie group $G$, is it possible it is a manifold with boundary? More generally, if $BG$ is infinite dimensional, is it possible it's approxiamted by manifolds with boundaries?

Approximate classyfing space by boundaryless manifolds?

As pointed out by Achim Krause, any finite CW complex is homotopy equivalent to a manifold with boundary (by embedding into ℝ𝑛 and thickening), and so every finite type CW complex can be approximated by manifolds with boundary.

Given a Lie group $G$, is it possible to approximate $BG$ by using boundaryless manifolds? For example, $BS^1$ can be approximated by $\mathbb{CP}^N$. Is this a general phenomenon or special case for torus? (The classfying space of torus supports a group structure, so it has to be boundaryless)

Source Link
0207
0207
  • 123
  • 1
  • 5

Is it possible the classyfing space is a manifold with boundary?

As the classfying space $BG$ of a Lie group $G$, is it possible it is a manifold with boundary? More generally, if $BG$ is infinite dimensional, is it possible it's approxiamted by manifolds with boundaries?