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          "value": "Center of Mathematics, Computation and Cognition, Universidade Federal do ABC, 09210-580, Santo Andr\u00e9, SP, Brazil"
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      "surname": "Fresneda", 
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      "full_name": "Fresneda, Rodrigo", 
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    {
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          "value": "Center of Mathematics, Computation and Cognition, Universidade Federal do ABC, 09210-580, Santo Andr\u00e9, SP, Brazil"
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      ], 
      "surname": "de Souza", 
      "email": "lucas.souza4799@gmail.com", 
      "full_name": "de Souza, Lucas", 
      "given_names": "Lucas"
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    {
      "surname": "Vassilevich", 
      "given_names": "Dmitri", 
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          "country": "Brazil", 
          "value": "Center of Mathematics, Computation and Cognition, Universidade Federal do ABC, 09210-580, Santo Andr\u00e9, SP, Brazil"
        }
      ], 
      "full_name": "Vassilevich, Dmitri", 
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      "source": "Elsevier", 
      "title": "Edge states and the Invariant"
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      "primary": "Physics Letters B"
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      "source": "Elsevier", 
      "value": "We propose a relation between the \u03b7 invariant on a manifold with boundary, the \u03b7 invariants of edge states, and the \u03b7 invariant in an infinite volume limit. With the example of planar fermions with bag and chiral bag boundary conditions we show that this relation holds whenever edge states are sufficiently well-localized near the boundary. As a by-product we show that the spectrum of edge modes for chiral bag boundary conditions is linear but bounded."
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