arXiv:1803.10982 Abstract | arXiv Analytics

arXiv:1803.10982 [math.DS]Abstract References Reviews Resources

Zeta Function at Zero for Surfaces with Boundary

Published 2018-03-29, updated 2018-07-25Version 2

We study the Ruelle zeta function at zero for negatively curved oriented surfaces with boundary. At zero, the zeta function has a zero and its multiplicity is shown to be determined by the Euler characteristic of the surface. This is shown by considering certain Ruelle resonances and identifying their multiplicity with dimensions of the relative cohomology of the surface.

Comments: 17 pages, clarification of map defined in Section 4, minor change in proof of injectivity

Categories: math.DS

Subjects: 37C30, 37D40, 58J50

Keywords: ruelle zeta function, multiplicity, euler characteristic, ruelle resonances, negatively curved oriented surfaces

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