Bulk and Boundary Invariants for Complex Topological Insulators by Emil Prodan & Hermann Schulz-Baldes

Author:Emil Prodan & Hermann Schulz-Baldes
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

where denotes the connected component of the unity. This tells that any element from the connect component of the unity of has a preimage in the connected component of the unity of . If v is a unitary from , then belongs to , hence there exists a unitary such that

The element so defined is called a lift and the standard notation is

The lift is unique up to homotopies. Next, one considers the projection

(4.9)

whose homotopy class is entirely determined by v and, moreover,

Since

and the short sequence (4.7) is exact, the projector (4.9) is in the image of in under . Throughout, we will identify and . Then the index map is defined as

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