Let S be a surface with genus g and n boundary components and let d(S) = 3g − 3 + n denote the number of curves in any pants decomposition of S. We employ metric properties of the graph of pants decompositions CP(S) prove that the Weil-Petersson metric on Teichmüller space Teich(S) is Gromov-hyperbolic if and only if d(S) ≤ 2. When d(S) ≥ 3 the Weil-Petersson metric has higher rank in the sense...

The first part of this work constructs positive-genus real Gromov-Witten invariants of realorientable symplectic manifolds of odd “complex” dimensions; the present part focuses on their properties that are essential for actually working with these invariants. We determine the compatibility of the orientations on the moduli spaces of real maps constructed in the first part with the standard node...

The Gromov-Wasserstein (GW) framework adapts ideas from optimal transport to allow for the comparison of probability distributions defined on different metric spaces. Scalable computation GW distances and associated matchings graphs point clouds have recently been made possible by state-of-the-art algorithms such as S-GWL MREC. Each these algorithmic breakthroughs relies decomposing underlying ...

In this paper, the concept of countably near PS-compactness inL-topological spaces is introduced, where L is a completely distributive latticewith an order-reversing involution. Countably near PS-compactness is definedfor arbitrary L-subsets and some of its fundamental properties are studied.

We give a complete solution for the reduced Gromov-Witten theory of resolved surface singularities of type An, for any genus, with arbitrary descendent insertions. We also present a partial evaluation of the T -equivariant relative Gromov-Witten theory of the threefold An × P 1 which, under a nondegeneracy hypothesis, yields a complete solution for the theory. The results given here allow compa...

In this paper we discuss the behavior of the Gromov boundaries and limit sets for the surface subgroups of the mapping class group with accidental parabolics constructed by the author and A. Reid (2006). Specifically, we show that generically there are no Cannon–Thurston maps from the Gromov boundary to Thurston’s boundary of Teichmüller space.

DOI: http://dx.doi.org/10.4314/tvl.v51i2.4 Visions of the future in the ‘new’ Swahili novel: Hope in desperation? Mikhail Gromov Mikhail D. Gromov is an Assistant Professor of Literature at the United States International University in Nairobi. He researches on literatures of Eastern and Southern Africa in English and indigenous languages, Swahili literature, comparative literature. Email: mgro...

I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack S(X). When X is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the Gromov-Witten invariants of a point.

In [3], Pandharipande studied the relationship between the enumerative geometry of certain 3-folds and the Gromov-Witten invariants. In some good cases, enumerative invariants (which are manifestly integers) can be expressed as a rational combination of Gromov-Witten invariants. Pandharipande speculated that the same combination of invariants should yield integers even when they do not have any...