2,161 research outputs found
Tautological classes on the moduli space of hyperelliptic curves with rational tails
We study tautological classes on the moduli space of stable n-pointed hyperelliptic curves of genus g with rational tails. The method is based on the approach of Yin in comparing tautological classes on the moduli of curves and the universal Jacobian. Our result gives a complete description of tautological relations. It is proven that all relations come from the Jacobian side. The intersection pairings are shown to be perfect in all degrees. We show that the tautological algebra coincides with its image in cohomology via the cycle class map. The latter is identified with monodromy invariant classes in cohomology. (C) 2017 Elsevier B.V. All rights reserved11sci
On the Domain of Applicability of General Relativity
We consider the domain of applicability of general relativity (GR), as a
classical theory of gravity, by considering its applications to a variety of
settings of physical interest as well as its relationship with real
observations. We argue that, as it stands, GR is deficient whether it is
treated as a microscopic or a macroscopic theory of gravity. We briefly discuss
some recent attempts at removing this shortcoming through the construction of a
macroscopic theory of gravity. We point out that such macroscopic extensions of
GR are likely to be non-unique and involve non-Riemannian geometrical
frameworks.Comment: 19 pages, LaTeX, submitted to Found. Phy
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