Related papers: CP^n, or, entanglement illustrated
This short and fairly informal note is an attempt to explain how methods of homological algebra may be brought to bear on problems in symplectic geometry. We do this by looking at a familiar sample question, which is that of the topology of…
We construct orbifolds with quasitoric boundary and show that they have stable almost complex structure. We show that a quasitoric orbifold is complex cobordant to finite disjoint copies of complex orbifold projective spaces. Finally some…
We consider proper-biharmonic flat tori with constant mean curvature (CMC) in spheres and find necessary and sufficient conditions for certain rectangular tori and square tori to admit full CMC proper-biharmonic immersions in…
We propose a definition of computable manifold by introducing computability as a structure that we impose to a given topological manifold, just in the same way as differentiability or piecewise linearity are defined for smooth and PL…
A representation of a finitely generated group into the projective general linear group is called convex co-compact if it has finite kernel and its image acts convex co-compactly on a properly convex domain in real projective space. We…
In this survey, we discuss whether the complex projective space can be characterized by its integral cohomology ring among compact complex manifolds.
We show that a closed simply connected 8-manifold (9-manifold) of positive sectional curvature on which a 3-torus (4-torus) acts isometrically is homeomorphic to a sphere, a complex projective space or a quaternionic projective plane…
Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
We extend T. Y. Thomas's approach to the projective structures, over the complex analytic category, by involving the $\rho$-connections. This way, a better control of the projective flatness is obtained and, consequently, we have, for…
We describe of the topology of the geometric quotients of 2n dimensional compact connected symplectic manifolds with n-1 dimensional torus actions. When the isotropy weights at each fixed point are in general position, the quotient is…
Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic…
In this paper we give examples of closed smooth submanifolds of RP^n which are isotopic to nonsingular projective subvarieties of RP^n but they can not be isotopic to the real parts of nonsingular complex projective subvarieties of CP^n.
We describe the integral equivariant cohomology ring of a weighted projective space in terms of piecewise polynomials, and thence by generators and relations. We deduce that the ring is a perfect invariant, and prove a Chern class formula…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
We define symmetric spaces in arbitrary dimension and over arbitrary non-discrete topological fields $\K$, and we construct manifolds and symmetric spaces associated to topological continuous quasi-inverse Jordan pairs and -triple systems.…
We introduce and study bipartite quantum states that are invariant under the local action of the cyclic sign group. Due to symmetry, these states are sparse and can be parameterized by a triple of vectors. Their important semi-definite…
A torus manifold is an even-dimensional manifold acted on by a half-dimensional torus with non-empty fixed point set and some additional orientation data. It may be considered as a far-reaching generalisation of toric manifolds from…
We prove that finite area isolated singularities of surfaces with constant positive curvature in R^3 are removable singularities, branch points or immersed conical singularities. We describe the space of immersed conical singularities of…
Let A be a line arrangement in the complex projective plane CP2. We define and describe the inclusion map of the boundary manifold --the boundary of a close regular neighborhood of A-- in the exterior of the arrangement. We obtain two…
A smooth quartic curve in the complex projective plane has 36 inequivalent representations as a symmetric determinant of linear forms and 63 representations as a sum of three squares. These correspond to Cayley octads and Steiner complexes…