Related papers: Symbols and equivariant birational geometry in sma…
There are (at least) two different approaches to define equivariant analogue of the Euler charateristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach…
We present alternative postulates for Euclidean geometry whose merit is that they lead to a new class of invariants and associated geometries for real finite-dimensional unital associative algebras.
We study equivariant unirationality of actions of finite groups on tori of small dimensions.
We develop a theory of Burnside rings in the context of birational equivalences of algebraic varieties equipped with logarithmic volume forms. We introduce a residue homomorphism and construct an additive invariant of birational morphisms.…
Topics concerning metric dimension related invariants in graphs are nowadays intensively studied. This compendium of combinatorial and computational results on this topic is an attempt of surveying those contributions that are of the…
A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally…
This paper introduces a novel framework for constructing invariants in $G$-equivariant birational geometry by unifying two recent approaches: the theory of atoms recently developed by Katzarkov, Kontsevich, Pantev, and Yu, and the theory of…
We use a recent advance in birational geometry to prove new lower bounds on the essential dimension of some finite groups.
We extend some of the measures of association defined by Lazarsfeld and Martin, obtaining useful invariants to compare the birational geometry of two varieties having different dimensions. We explore such invariants providing examples and…
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…
In this article we discuss some general results on the covariant Picard groupoid in the context of differential geometry and interpret the problem of lifting Lie algebra actions to line bundles in the Picard groupoid approach.
We introduce a new isomorphism invariant for generalized Baumslag-Solitar (GBS) groups, which we call the limit angle. Unlike previously known invariants, which are primarily algebraic, the limit angle admits a dynamical interpretation,…
In this note, we present a new look at translationally equivariant minimal Lagrangian surfaces in the complex projective plane via the loop group method.
Group theory indicates the existence of a $SO(8) X SO(7) \subset SO(16)$ invariant self-duality equation for a 3-form in 16 dimensions. It is a signal for interesting topological field theories, especially on 8-dimensional manifolds with…
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
Equivariant versions of the radial index and of the GSV-index of a vector field or a 1-form on a singular variety with an action of a finite group are defined. They have values in the Burnside ring of the group. Poincar\'e-Hopf type…
In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…
A new local, covariant and nilpotent symmetry is shown to exist for the interacting BRST invariant U(1) gauge theory in two dimensions of space-time. Under this new symmetry, it is the gauge-fixing term that remains invariant and the…
Bargmann invariants, a class of gauge-invariant quantities arising from the overlaps of quantum state vectors, provide a profound and unifying framework for understanding the geometric structure of quantum mechanics. This survey offers a…
The recently introduced equivariant BV formalism is extended to the case of manifolds with boundary under appropriate conditions. AKSZ theories are presented as a practical example.