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Entropy bounds and second cohomology

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When X is a finite complex and \(\pi_{1}X\) acts on \({\mathbb{R}}^2\) by translations we give criteria involving H2X for an equivariant map \(F : \tilde{X} \rightarrow {\mathbb{R}}^2\) to be onto. Following work of Manning and Shub, this leads to entropy bounds related to Shub’s entropy conjecture.

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Correspondence to David Fried.

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Dedicated to Steve Smale in honor of his 80th birthday

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Fried, D. Entropy bounds and second cohomology. J. fixed point theory appl. 6, 87 (2009). https://doi.org/10.1007/s11784-009-0120-y

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  • DOI: https://doi.org/10.1007/s11784-009-0120-y

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