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annie marie cœur
annie marie cœur
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In this paperpaper also the journal front page, eq. 2.14, it introduces the the Grothendieck group $K^0$ of the category of boundary conditions of topological field theory.

enter image description here

My question is that

  • what exactly is the Grothendieck group $K^0$ of the category of boundary conditions of topological field theory really mean?
  • Does this say that the boundary conditions of topological field theory can be related or classified by a Grothendieck group? Is this an abelian group or nonabelian group? ($K^0(BCondμ(M^{d−1}) )=?$)
  • Should the boundary conditions of topological field theory classified by some bimodule of certain modular tensor category? how is this related to a Grothendieck group?

In this paper also the journal front page, eq. 2.14, it introduces the the Grothendieck group $K^0$ of the category of boundary conditions of topological field theory.

enter image description here

My question is that

  • what exactly is the Grothendieck group $K^0$ of the category of boundary conditions of topological field theory really mean?
  • Does this say that the boundary conditions of topological field theory can be related or classified by a Grothendieck group? Is this an abelian group or nonabelian group? ($K^0(BCondμ(M^{d−1}) )=?$)
  • Should the boundary conditions of topological field theory classified by some bimodule of certain modular tensor category? how is this related to a Grothendieck group?

In this paper also the journal front page, eq. 2.14, it introduces the Grothendieck group $K^0$ of the category of boundary conditions of topological field theory.

enter image description here

My question is that

  • what exactly is the Grothendieck group $K^0$ of the category of boundary conditions of topological field theory really mean?
  • Does this say that the boundary conditions of topological field theory can be related or classified by a Grothendieck group? Is this an abelian group or nonabelian group? ($K^0(BCondμ(M^{d−1}) )=?$)
  • Should the boundary conditions of topological field theory classified by some bimodule of certain modular tensor category? how is this related to a Grothendieck group?
Source Link
annie marie cœur
annie marie cœur
  • 2.1k
  • 9
  • 20

Grothendieck group of the category of boundary conditions of topological field theory

In this paper also the journal front page, eq. 2.14, it introduces the the Grothendieck group $K^0$ of the category of boundary conditions of topological field theory.

enter image description here

My question is that

  • what exactly is the Grothendieck group $K^0$ of the category of boundary conditions of topological field theory really mean?
  • Does this say that the boundary conditions of topological field theory can be related or classified by a Grothendieck group? Is this an abelian group or nonabelian group? ($K^0(BCondμ(M^{d−1}) )=?$)
  • Should the boundary conditions of topological field theory classified by some bimodule of certain modular tensor category? how is this related to a Grothendieck group?