Related papers: New Techniques for obtaining Schubert-type formula…

A natural way of generalising Hamiltonian toric manifolds is to permit the presence of generic isolated singularities for the moment map. For a class of such ``almost-toric 4-manifolds'' which admits a Hamiltonian $S^1$-action we show that…

We construct Steinberg summands of $G$-equivariant spectra with $\mathrm{GL}_n(\mathbb{F}_p)$-action. We prove a lemma about their fixed points when $G$ is a $p$-group, and then use this lemma to compute the fixed points of the Steinberg…

We extend a classical result of Caughran/Schwartz and another recent result of Gunatillake by showing that if D is a bounded, convex domain in n-dimensional complex space, m is a holomorphic function on D and bounded away from zero toward…

We use symplectic cobordism, and the localization result of Ginzburg, Guillemin, and Karshon, to find a wall-crossing formula for the signature of regular symplectic quotients of Hamiltonian torus actions. The formula is recursive,…

This work constitutes the second part of a series of studies that aim to utilise tools from Hamiltonian mechanics to investigate the motion of an extended body in general relativity. The first part of this work [Refs. [1, 2]] constructed a…

We present a simple approach to questions of topological orbit equivalence for actions of countable groups on topological and smooth manifolds. For example, for any action of a countable group $\Gamma$ on a topological manifold where the…

Let V be a 2n-dimensional complex symplectic space. Let G' be the Lagrangian Grassmannian of maximal isotropic subspaces of V embedded via the inclusion i into the Grassmannian G of all n-dimensional subspaces of V. We discuss the…

We study the equivariant oriented cohomology ring $h_T(G/P)$ of partial flag varieties using the moment map approach. We define the right Hecke action on this cohomology ring, and then prove that the respective Bott-Samelson classes in…

We establish left and right canonical factorizations of Hilbert-space operator-valued functions G(z) that are analytic on neighborhoods of the complex unit circle and the origin 0, and that have the form G(z)=I+F(z) with F(z) taking…

In this paper, we propose a novel framework for efficiently and accurately estimating Lipschitz constants in hybrid quantum-classical decision models. Our approach integrates classical neural network with quantum variational circuits to…

In the context of orientable circuits and subcomplexes of these as representing certain singular spaces, we consider characteristic class formulas generalizing those classical results as seen for the Riemann-Hurwitz formula for regulating…

Let $M$ be a compact 3-manifold and $\Gamma=\pi_1(M)$. Work of Thurston and Culler--Shalen established the $\mathrm{SL}_2(\mathbb{C})$ character variety $X(\Gamma)$ as fundamental tool in the study of the geometry and topology of $M$. This…

We establish the formula for multiplication by the class of a special Schubert variety in the integral cohomology ring of the flag manifold. This formula also describes the multiplication of a Schubert polynomial by either an elementary…

Let M be a compact Kaehler manifold equipped with a Hamiltonian action of a compact Lie group G. In [Invent. Math. 67 (1982), no.~3, 515--538], Guillemin and Sternberg showed that there is a geometrically natural isomorphism between the…

In a previous paper Affine symmetries of the equivariant quantum cohomology of rational homogeneous spaces, a general formula was given for the multiplication by some special Schubert classes in the quantum cohomology of any homogeneous…

We generalise the Atiyah-Segal-Singer fixed point theorem to noncompact manifolds. Using $KK$-theory, we extend the equivariant index to the noncompact setting, and obtain a fixed point formula for it. The fixed point formula is the…

The Hilbert space of a free massless particle moving on a group manifold is studied in details using canonical quantisation. While the simplest model is invariant under a global symmetry, $G \times G$, there is a very natural way to…

The paper is devoted to "uniform" reduction of smooth functions on 2-manifolds to canonical form near critical points by some coordinate changes in some neighbourhoods of these points. For singularity types $E_6,E_8$ and $A_n$, we…

Exact canonically conjugate momenta Pi_{2mu} in quadrupole nuclear collective motions are proposed. The basic idea lies in the introduction of a discrete integral equation for the strict definition of canonically conjugate momenta to…

Let $M$ be a smooth manifold and $G$ a compact connected Lie group acting on $M$ by isometries. In this paper, we study the equivariant cohomology of ${\bf X}=T^\ast M$, and relate it to the cohomology of the Marsden-Weinstein reduced space…