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Abstract Under finite regular covering spaces, each preimage class of the base spaces is covered by some preimage classes of the covering spaces. We find an explicit relationship between those… Click to show full abstract
Abstract Under finite regular covering spaces, each preimage class of the base spaces is covered by some preimage classes of the covering spaces. We find an explicit relationship between those preimage classes in terms of covering transformation groups. Thereby we obtain a relationship of the homomorphism indices between them in terms of covering transformation groups. This is a local averaging formula and is the main result of our paper. The local formula gives rise to a global formula for the preimage homomorphism index and a formula for the preimage Reidemeister trace.
Journal Title: Topology and its Applications
Year Published: 2021
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