Covering Systems, Solenoids, and Shape Theory

Details Covering Systems, Solenoids, and Shape Theory Covering Systems, Solenoids, and Shape Theory

2010-09-28

arxiv.org/abs/1009.5716v3

Mathematics

Geometric Topology

The paper has been withdrawn due to an error in Theorem 4.1, which is false as stated. We will resbumit this work once the err

Scientific paper

We use basic results from shape theory to investigate inverse systems of covers and the corresponding fundamental pro-groups. Many of the standard shape-theoretic definitions become simpler in the context of covering systems and filtered groups, and we develop the theory largely within this context. We give several applications, including a classification of maps between P-adic solenoids up to homotopy. Also, we develop a description of the group of homotopy self-equivalences for certain aspherical solenoids, expanding on a result of Odden regarding the universal hypebolic solenoid.

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