arXiv research

The study proves a localization theorem and calculates volumes for superspaces.

We calculate the volumes of the hyperbolic twist knot cone-manifolds using the Schläfli formula. Even though general ideas for calculating the volumes of cone-manifolds are around, since there is no concrete calculation written, we present here the concrete calculations. We express the length of the singular locus in t…

The paper calculates intertwiners for a torus and proves a conjecture about their limits.

We provide methods to compute the colored HOMFLY polynomials of knots and links with symmetric representations based on the linear skein theory. By using diagrammatic calculations, several formulae for the colored HOMFLY polynomials are obtained. As an application, we calculate some examples for hyperbolic knots and li…

We calculate the volume of the $7_3^2$ link cone-manifolds using the Schläfli formula. As an application, we give the volume of the cyclic coverings over the link.

We calculate the volume entropy of local Hermitian symmetric spaces of noncompact type in terms of its invariant $r$, $a$, $b$.

In a noncommutative torus, effect of perturbation by inner derivation on the associated quantum stochastic process and geometric parameters like volume and scalar curvature have been studied. Cohomological calculations show that the above perturbation produces new spectral triples. Also for the Weyl C^*-algebra, the La…

In arxiv:1205.1274 Rieck and Yamashita defined the link volume of 3-manifolds and studied some of its basic properties. Many of these properties are similar to the corresponding properties of the hyperbolic volume. In this paper we calculate the link volume of an infinite family of prism manifolds. As a corollary, we s…

New formula calculates volumes of ideal hyperbolic drums.

New recursion found for hyperbolic sphere volumes.

The paper generalizes the second Pappus-Guldin theorem for calculating volumes of bodies.

Yokota suggested an optimistic limit method of the Kashaev invariants of hyperbolic knots and showed it determines the complex volumes of the knots. His method is very effective and gives almost combinatorial method of calculating the complex volumes. However, to describe the triangulation of the knot complement, he re…

Method calculates function integrals on complex manifolds.

New hyperbolic polyhedra with $π/3$ angles and volumes calculated.

In this article we describe cell decompositions of the moduli space of Riemann surfaces and their relationship to a Hurwitz problem. The cells possess natural linear structures and with respect to this they can be described as rational convex polytopes which come equipped with natural integer points and a volume form. …

Integral foliated simplicial volume is a version of simplicial volume combining the rigidity of integral coefficients with the flexibility of measure spaces. In this article, using the language of measure equivalence of groups we prove a proportionality principle for integral foliated simplicial volume for aspherical m…

We study hyperbolic bongles and find their volumes.

Study of $p$-adic simplicial volumes and their properties.

Formula calculates volume of two-bridge knots.

Study calculates volumes of Fano K-moduli spaces in various dimensions.

Study on volume growth of horospheres in specific Heintze groups.

We present a systematic calculation of the volumes of compact manifolds which appear in physics: spheres, projective spaces, group manifolds and generalized flag manifolds. In each case we state what we believe is the most natural scale or normalization of the manifold, that is, the generalization of the unit radius co…

A technique to calculate the colored Jones polynomials of satellite knots, illustrated by the Whitehead doubles of knots, is presented. Then we prove the volume conjecture for Whitehead doubles of a family of torus knots and show some interesting observations.

The paper confirms a conjecture linking link bipyramid volume and Mahler measure.

We calculate finite volumes of moduli spaces of flat surfaces with conical singularities.

New method constructs non-arithmetic hyperbolic orbifolds from complex arithmetic ball quotients.

The paper calculates super Weil-Petersson volumes for large genus.

New Crofton formulae derived from existing ones.

We introduce a natural definition of the renormalized volume of a 4-dimensional Ricci-flat ALE space. We then prove that the renormalized volume is always less or equal than zero, with equality if and only if the ALE space is isometric to its asymptotic cone. Currently the only known examples of 4-dimensional Ricci-fla…

We describe a natural strategy to enumerate compact hyperbolic 3-manifolds with geodesic boundary in increasing order of complexity. We show that the same strategy can be employed to analyze simultaneously compact manifolds and finite-volume manifolds having toric cusps. In opposition to this we show that, if one allow…

We calculate the Masur-Veech volume of the gothic locus $\mathcal{G}$ in the stratum $\mathcal{H}(2^{3})$ of genus four. Our method is based on the use of the formulae for the Euler characteristics of gothic Teichmüller curves to determine the number of lattice points of given area. We also use this method to recalcula…

The paper calculates the volume growth of hyperbolic surfaces with short geodesics.

I show various calculations of the limit of the colored Jones function for the figure-eight knot and confirm R. Kashaev's conjecture in this case.

I calculate optimistically asymptotic behaviors of the WRT SU(2) invariants for the three-manifolds obtained from the figure-eight knot by p-surgeries with p=0,1,2,...,10, from which one can extract volumes and the Chern-Simons invariants of these closed manifolds. I conjecture that this also holds for general closed t…

The paper calculates transformation operators and proves a theorem on 4D manifolds.

Study calculates reach and curvature of a specific geometric variety.

By work of W. Thurston, knots and links in the 3-sphere are known to either be torus links, or to contain an essential torus in their complement, or to be hyperbolic, in which case a unique hyperbolic volume can be calculated for their complement. We employ a construction of Turaev to associate a family of hyperbolic 3…

New chaos formula simplifies variance calculation for Gaussian nodal volumes.

Study of $n$-cylinder surfaces to calculate Masur-Veech volumes.

Researchers introduce a family of hyperbolic Brunnian links and calculate their volumes.

Researchers calculate the volume of Seifert representations for graph manifolds and their covers.

The article presents calculations that prove practical importance of the earlier derived theoretical relationship between the interest rate on the interbank credit market, volume of investment and the quantity of securities tradable on the stock exchange.

Improved learning of probabilistic box embeddings by modeling parameters with Gumbel distributions.

We obtain a formula for the Turaev-Viro invariants of a link complement in terms of values of the colored Jones polynomial of the link. As an application we give the first examples for which the volume conjecture of Chen and the third named author\,\cite{Chen-Yang} is verified. Namely, we show that the asymptotics of t…

Formula calculates volume of CMC surfaces with translational periods, disproving isoperimetric conjecture.

We calculate the asymptotic behavior of hyperbolic volume and Chern-Simons invariant.

Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide algebraically on the category of CW-complexes. It is the aim of this paper to prove that…

New method calculates Ricci curvature from distances between weighted volumes.