Skip to main content
MathOverflow

Return to Question

formatting, added tag
Source Link
YCor
YCor
  • 63.9k
  • 5
  • 187
  • 286

Moduli Spacespace of Flatflat connection over Homologyhomology 3-Shperesphere

I'm trying to understand the space of flat connections of the trivial $SU(2)$$\mathrm{SU}(2)$-bundle over a closed, oriented homology three-sphere (for the purpose of understanding the instanton Floer homology of it).

From now on I will just define the space of gauge equivalent classes of flat connections on it to be $R$.

Are the following facts correct and why?

  1. The trivial connection is the only reducible connection.

  2. $R$ is isolated generically (according to the perturbation of Chern-Simons functional)

  3. $R$ is compact.

Moduli Space of Flat connection over Homology 3-Shpere

I'm trying to understand the space of flat connections of the trivial $SU(2)$-bundle over a closed, oriented homology three-sphere (for the purpose of understanding the instanton Floer homology of it).

From now on I will just define the space of gauge equivalent classes of flat connections on it to be $R$.

Are the following facts correct and why?

  1. The trivial connection is the only reducible connection.

  2. $R$ is isolated generically (according to the perturbation of Chern-Simons functional)

  3. $R$ is compact.

Moduli space of flat connection over homology 3-sphere

I'm trying to understand the space of flat connections of the trivial $\mathrm{SU}(2)$-bundle over a closed, oriented homology three-sphere (for the purpose of understanding the instanton Floer homology of it).

From now on I will just define the space of gauge equivalent classes of flat connections on it to be $R$.

Are the following facts correct and why?

  1. The trivial connection is the only reducible connection.

  2. $R$ is isolated generically (according to the perturbation of Chern-Simons functional)

  3. $R$ is compact.

added 28 characters in body
Source Link
Lamda8
Lamda8
  • 181
  • 4

I'm trying to understand the space of flat connections overof the trivial $SU(2)$-bundle over a closed, oriented homology three-sphere (for the purpose of understanding the instanton Floer homology of it).

From now on I will just define the space of gauge equivalent classes of flat connections on it to be $R$.

Are the following facts correct and why?

  1. The trivial connection is the only reducible connection.

  2. $R$ is isolated generically (according to the perturbation of Chern-Simons functional)

  3. $R$ is compact.

I'm trying to understand the space of flat connections over the closed, oriented homology three-sphere (for the purpose of understanding the instanton Floer homology of it).

From now on I will just define the space of gauge equivalent classes of flat connections on it to be $R$.

Are the following facts correct and why?

  1. The trivial connection is the only reducible connection.

  2. $R$ is isolated generically (according to the perturbation of Chern-Simons functional)

  3. $R$ is compact.

I'm trying to understand the space of flat connections of the trivial $SU(2)$-bundle over a closed, oriented homology three-sphere (for the purpose of understanding the instanton Floer homology of it).

From now on I will just define the space of gauge equivalent classes of flat connections on it to be $R$.

Are the following facts correct and why?

  1. The trivial connection is the only reducible connection.

  2. $R$ is isolated generically (according to the perturbation of Chern-Simons functional)

  3. $R$ is compact.

Source Link
Lamda8
Lamda8
  • 181
  • 4

Moduli Space of Flat connection over Homology 3-Shpere

I'm trying to understand the space of flat connections over the closed, oriented homology three-sphere (for the purpose of understanding the instanton Floer homology of it).

From now on I will just define the space of gauge equivalent classes of flat connections on it to be $R$.

Are the following facts correct and why?

  1. The trivial connection is the only reducible connection.

  2. $R$ is isolated generically (according to the perturbation of Chern-Simons functional)

  3. $R$ is compact.