Related papers: Lusternik-Schnirelmann theory to Topological Compl…
We derive a model of constrained topological gravity, a theory recently introduced by us through the twist of N=2 Liouville theory, starting from the general BRST algebra and imposing the moduli space constraint as a gauge fixing. To do…
In this paper, we investigate discrete topological complexity $TC(K)$ introduced for situations where the configuration space possesses a simplicial structure. %Simplicial complexes are well-known and commonly used in programming for…
We show that there exists a canonical topology, naturally connected with the causal site of J. D. Christensen and L. Crane, a pointless algebraic structure motivated by quantum gravity. Taking a causal site compatible with Minkowski space,…
A topological version of Levinson's theorem is presented. Its proof relies on a C*-algebraic framework which is introduced in detail. Various scattering systems are considered in this framework, and more coherent explanations for the…
The rising complexity of our terrestrial surrounding is an empirical fact. Details of this process evaded description in terms of physics for long time attracting attention and creating myriad of ideas including non-scientific ones. In this…
Although it has been a well-known fact, for more than two decades, that category theory is needed for the study of topological orders, it is still a non-trivial challenge for students and working physicists to master the abstract language…
We give bounds for the module sectional category of products of maps which generalise a theorem of Jessup for Lusternik-Schnirelmann category. We deduce also a proof of a Ganea type conjecture for topological complexity. This is a first…
Motivated by ideas from string theory and quantum field theory new invariants of knots and 3-dimensional manifolds have been constructed from complex algebraic structures such as Hopf algebras (Reshetikhin and Turaev), monoidal categories…
We explore the symmetry structure of Type II Little String Theories and their T-dualities. We construct these theories both from the bottom-up perspective starting with seed Superconformal Field Theories, and from the top-down using…
We present upper and lower bounds for symmetrized topological complexity $TC^\Sigma(X)$ in the sense of Basabe-Gonz\'alez-Rudyak-Tamaki. The upper bound comes from equivariant obstruction theory, and the lower bounds from the cohomology of…
The topology of the causal boundary for standard static spacetimes--spacetimes time-invariantly conformal to a metric product of the Lorentz line and a Riemannian manifold--is studied in depth. As this is given in terms of a set of…
Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete…
Following recent works on corner charges we investigate the boundary structure in the case of the theory of gravity formulated as a constrained BF theory. This allows us not only to introduce the cosmological constant, but also explore the…
In gravity theories that exhibit spontaneous scalarization, astrophysical objects are identical to their general relativistic counterpart until they reach a certain threshold in compactness or curvature. Beyond this threshold, they acquire…
In this article we study a homotopy invariant cat(X,B,\xi) on a pair of finite CW complexes with respect to a continuous closed 1-form. This is a generalisation of a Lusternik-Schnirelmann category developed by Farber, studying the topology…
We revisit the work of To\"en--Vezzosi and Lurie on Grothendieck topologies, using the new tools of acyclic classes and congruences. We introduce a notion of extended Grothendieck topology on any $\infty$-topos, and prove that the poset of…
We compute the Lusternik-Schnirelmann category (LS-cat) and the higher topological complexity ($TC_s$, $s\geq2$) of the "no-$k$-equal" configuration space Conf$_k(\mathbb{R},n)$. This yields (with $k=3$) the LS-cat and the higher…
We reconsider two-dimensional topological gravity in a functional and lagrangian framework. We derive its Slavnov-Taylor identities and discuss its (in)dependence on the background gauge. Correlators of reparamerization invariant…
We present generalizations of the spin Sutherland systems obtained earlier by Blom and Langmann and by Polychronakos in two different ways: from SU(n) Yang--Mills theory on the cylinder and by constraining geodesic motion on the N-fold…
Farber introduced a notion of topological complexity $\TC(X)$ that is related to robotics. Here we introduce a series of numerical invariants $\TC_n(X), n=1,2, ...$ such that $\TC_2(X)=\TC(X)$ and $\TC_n(X)\le \TC_{n+1}(X)$. For these…