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Is the square diagram of index and exponential maps in $K$-theory of $C^*$-algebras anti-commutative?

Assume we have a $3\times 3$ grid with rows and columns being short exact sequences of $C^*$-algebras. This gives a grid of 6-term exact sequences: 3 "horizontal" sequences and 3 "vertical" sequences,...

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modified Nov 26, 2014 at 9:22

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Is the square diagram of index and exponential maps in $K$-theory of $C^*$-algebras anti-commutative?

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Is the square diagram of index and exponential maps in $K$-theory of $C^*$-algebras anti-commutative?

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