Related papers: Differential topology interacts with isoparametric…
Recent results concerning the relation of topology and low-lying fermion modes are summarized.
The correspondence between two geometrical descriptions of the KP-hierarchy, one by discrete surface and another by difference analogue of differential geometry, is given.
We prove a result which establishes restrictions on the pseudoholomorphic curves which can exist in a stable Hamiltonian manifold in the presence of certain $\mathbb{R}$-invariant foliations of the symplectization by holomorphic…
A concept of a rectangular diagram of a foliation in the three-sphere is introduced. It is shown that any co-orientable finite depth foliation in the complement of a link admits a presentation by a rectangular diagram compatible with the…
We provide a classification of complex projective surfaces with a holomorphic foliation whose group of birational symetries is infinite.
We develop the deformation theory of symplectic foliations, i.e. regular foliations equipped with a leafwise symplectic form. The main result of this paper is that each symplectic foliation has an attached $L_\infty$-algebra controlling its…
Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational…
We establish that the intersection number between the horizontal foliations of any two finite-area holomorphic quadratic differentials on an arbitrary Riemann surface is finite. Our main result shows that the intersection number is jointly…
Contact-aware topology optimization faces challenges in robustness, accuracy, and applicability to internal structural surfaces under self-contact. This work builds on the recently proposed barrier-based Incremental Potential Contact (IPC)…
We construct isoperimetric regions from separating hypersurfaces in closed manifolds. This yields isoperimetric boundaries exhibiting a wide variety of topological types and singular sets.
Band-topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wavefunctions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an…
At sufficiently low temperatures and high densities, repulsive spherical particles in two-dimensions (2d) form close-packed structures with six-fold symmetry. By contrast, when the interparticle interaction has an attractive anisotropic…
A topology is introduced on spaces of Legendrian submanifolds and groups of contactomorphisms. The definition is motivated by the Alexandrov topology in Lorentz geometry.
Using tools and concepts from contact topology we show that non-vanishing twist implies conservation of the layer structure in cholesteric liquid crystals. This leads to a number of additional topological invariants for cholesteric…
Following ideas from a preprint of the second author, see [2], we investigate relations of dynamical Teichmuller spaces with dynamical objects. We also establish some connections with the theory of deformations of inverse limits and…
Isoparametric hypersurfaces and their application to special geometries
A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
This text arises from teaching advanced undergraduate courses in differential topology for the master curriculum in Mathematics at the University of Pisa. So it is mainly addressed to motivated and collaborative master undergraduate…
In this paper we consider planar polygons with parallel opposite sides. This type of polygons can be regarded as discretizations of closed convex planar curves by taking tangent lines at samples with pairwise parallel tangents. For this…
In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between…