Results 31 to 40 of about 2,939,402 (89)
Ribbons: Their Geometry and Topology [PDF]
Computer-Aided Design and Applications, 2004 AbstractRibbons may be used for the modeling of DNAs and proteins. The topology of a ribbon can be described by the link Lk, while its geometry is represented by the writhe Wr and the twist Tw. These three quantities are numerical integrals and are related by a single formula from knot theory.
T. C. Woo, C. K. Au
openaire +2 more sources
Lectures on families of Dirac operators and applications [PDF]
arXiv, 2022 These are the notes for a minicourse taught at the 2022 ICTP summer school `Frontiers in Geometry and Topology'. The goal is to introduce families of Dirac operators and how they can be used to study interactions between geometry and topology. In particular, we discuss the index theorem for families of twisted Dirac operators, and its applications to ...
arxiv
Quantum Foam and Topological Strings
, 2003 We find an interpretation of the recent connection found between topological strings on Calabi-Yau threefolds and crystal melting: Summing over statistical mechanical configuration of melting crystal is equivalent to a quantum gravitational path integral
A. Okounkov +28 more
core +3 more sources
Topology and Geometry of Spin Origami
Physical Review Letters, 2018 Kagome antiferromagnets are known to be highly frustrated and degenerate when they possess simple, isotropic interactions. We consider the entire class of these magnets when their interactions are spatially anisotropic. We do so by identifying a certain class of systems whose degenerate ground states can be mapped onto the folding motions of a ...
Michael J. Lawler +6 more
openaire +5 more sources
Billey's formula in combinatorics, geometry, and topology [PDF]
, 2013 In this expository paper we describe a powerful combinatorial formula and its implications in geometry, topology, and algebra. This formula first appeared in the appendix of a book by Andersen, Jantzen, and Soergel.
Tymoczko, Julianna S.
core +2 more sources
On the Alexandrov Topology of sub-Lorentzian Manifolds
, 2013 It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation ...
A Korolko +18 more
core +1 more source
Topological torus fibrations on Calabi--Yau manifolds via Kato--Nakayama spaces [PDF]
Proceedings of the G\"okova Geometry-Topology Conferences
2018/2019, published in 2021, 2020 This is an expository article on the Gross--Siebert approach to mirror symmetry and its interactions with the Strominger--Yau--Zaslow conjecture from a topological perspective.
arxiv
Stochastic geometry and topology of non-Gaussian fields
, 2012 Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter
A. M. Turner +10 more
core +2 more sources
Thom series of contact singularities [PDF]
, 2010 Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry (enumerative geometry, moduli spaces) and algebraic ...
Fehér, L. M., Rimányi, R.
core
Analytic Topology of Groups, Actions, Strings and Varietes [PDF]
arXiv, 2000 This is a paper in Analytic Topology.
arxiv