Related papers: Identities on Hyperbolic Manifolds

In this paper we mainly pay attention to the complex hyperbolic triangle groups of type (m, n, infinity) and discuss the discreteness. From the results more explicit conclusions about the triangle groups of type (n, infinity, infinity) will…

For a single cusped hyperbolic 3-manifold, Hodgson proved that there are only finitely many Dehn fillings of it whose trace fields have bounded degree. In this paper, we conjecture the same for manifolds with more cusps, and give the first…

The interaction between combinatorics and algebraic and differential geometry is very strong. While researching a problem of Hessian topology, we came across a series of identities of binomial coefficients, which are useful for proving a…

This part is a continuation of the Part I where we built resolutions of identity for certain non-Hermitian Hamiltonians constructed of biorthogonal sets of their eigen- and associated functions for the spectral problem defined on entire…

In this paper,based on the available mathematical works on geometry and topology of hyperbolic manifolds and discrete groups, some results of Freedman et al (hep-th/9804058) are reproduced and broadly generalized. Among many new results the…

We give an elementary proof of some identities that express the squares of Riemann zeta function at integer points in terms of the series involving hyperbolic functions, digamma function, Bernoulli numbers etc. In this version, inaccuracies…

We examine four identities conjectured by Hickerson which complement five modulo $9$ Kanade--Russell identities, and we build up a profile of new identities and new conjectures not unlike those found by Uncu and Zudilin.

We derive generalizations of McShane's identity for higher ranked surface group representations by studying a family of mapping class group invariant functions introduced by Goncharov and Shen which generalize the notion of horocycle…

We give a simple unified proof for all existing rational hypergeometric Ramanujan identities for $1/\pi$, and give a complete survey (without proof) of several generalizations: rational hypergeometric identities for $1/\pi^c$, Taylor…

In this expository note, we illustrate phenomena and conjectures about boundaries of hyperbolic groups by considering the special cases of certain amalgams of hyperbolic groups. While doing so, we describe fundamental results on hyperbolic…

In this paper, we classify completely hyperbolic 3-manifolds corresponding to geometric limits of Kleinian surface groups isomorphic to $\pi_1(S)$ for a finite-type hyperbolic surface $S$. In the first of the three main theorems, we…

This is the first in a series of papers showing that Haken manifolds have hyperbolic structures; this first was published, the second two have existed only in preprint form, and later preprints were never completed. This eprint is only an…

Using Ramanujan's identities and the Weierstrass-Enneper representation of minimal surfaces and the analogue for Born-Infeld solitons, we derive further non-trivial identities.

Given complex numbers $m_1,l_1$ and positive integers $m_2,l_2$, such that $m_1+m_2=l_1+l_2$, we define $l_2$-dimensional hypergeometric integrals $I_{a,b}(z;m_1,m_2,l_1,l_2)$, $a,b=0,...,\min(m_2,l_2)$, depending on a complex parameter…

We prove that for every countable group G there exists a hyperbolic 3-manifold M such that the isometry group of M, the mapping class group of M, and the outer automorphism group of the fundamental group of M are isomorphic to G.

This paper examines the representations of hyperbolic integral homology spheres into the binary icosahedral group $2I$. We specifically give a geometric meaning to $2I$ representations by relating them to Larsen's notion of quotient…

We develop the theory of multiplicative Ehresmann connections for Lie groupoid submersions covering the identity, as well as their infinitesimal counterparts. We construct obstructions to the existence of such connections, and we prove…

Behrstock, Hagen, and Sisto classified 3-manifold groups admitting a hierarchically hyperbolic space structure. However, these structures were not always equivariant with respect to the group. In this paper, we classify 3-manifold groups…

We study fixed point sets for holomorphic automorphisms (and endomorphisms) on complex manifolds. The main object of our interest is to determine the number and configuration of fixed points that forces an automorphism (endomorphism) to be…

We investigate relation between Dehn fillings and commensurability of hyperbolic 3-manifolds. The set consisting of the commensurability classes of hyperbolic 3-manifolds admits the quotient topology induced by the geometric topology. We…