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Topological Approach to Quantum Surfaces
Communications in Mathematical Physics, 1999A topological approach to quantisation of closed surfaces is presented. This is done by imposing the following ``minimal'' requirements for a quantisation \(R\) of a closed Riemann surface \(\Sigma\) of genus \(g\geq 2\): \(R\) is a unital \(C^*\)-algebra, both \(R\) and \(C(\Sigma)\) are fibres in a continuous family of \(C^*\)-algebras over a path ...
Natsume, Toshikazu, Nest, Ryszard
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, 2013
This chapter briefly reviews the fundamental concepts and theorems in algebraic topology [1], surface differential geometry [6], and surface Ricci flow [4, 7]. Detailed discussion on Ricci flow on general Riemannian manifolds can be found in [5]. Advanced topics on differential geometry related to Yamabe equations can be found in [9].
W. Zeng, X. Gu
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This chapter briefly reviews the fundamental concepts and theorems in algebraic topology [1], surface differential geometry [6], and surface Ricci flow [4, 7]. Detailed discussion on Ricci flow on general Riemannian manifolds can be found in [5]. Advanced topics on differential geometry related to Yamabe equations can be found in [9].
W. Zeng, X. Gu
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Codazzi Tensors and the Topology of Surfaces [PDF]
Annals of Global Analysis and Geometry, 1998 The authors introduce the notion of \((0,m)\)-Codazzi tensors relative to an affine connection which extends the well-known concept for \(m=2\). The main results are as follows. (1) Let \(M\) be a compact, oriented surface of genus \(\gamma\), and let \(g\) be a Riemannian metric on \(M\). For \(m\geq 2\) define the \(R\)-vector space \({\mathcal R}_m:
Udo Simon, Huili Liu, C. P. Wang
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1995
Our aim in this section is to show that a compact orientable surface is homeomorphic to a sphere with handles, under the assumption that the surface can be triangulated. The idea is to “flatten” it out, to realize the surface as a polygon in the plane, with certain identifications on the boundary edges, and then, by cutting and pasting, to simplify ...
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Our aim in this section is to show that a compact orientable surface is homeomorphic to a sphere with handles, under the assumption that the surface can be triangulated. The idea is to “flatten” it out, to realize the surface as a polygon in the plane, with certain identifications on the boundary edges, and then, by cutting and pasting, to simplify ...
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Tumors evade immune cytotoxicity by altering the surface topology of NK cells
Nature Immunology, 2023Xiaohu Zheng +13 more
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On Topological Classification of A-Diffeomorphisms of Surfaces [PDF]
Journal of Dynamical and Control Systems, 2000 This paper is a review of results obtained by the author and related to the topological classification of discrete dynamical systems (cascades) defined on an orientable smooth closed surface \({\mathcal A}_g\) of genus \(g\geq 0\). Topics are: 1) topological classification of one-dimensional basic sets via automorphisms of fundamental groups, 2 ...
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On-surface synthesis of graphene nanoribbons with zigzag edge topology
Nature, 2015Graphene-based nanostructures exhibit electronic properties that are not present in extended graphene. For example, quantum confinement in carbon nanotubes and armchair graphene nanoribbons leads to the opening of substantial electronic bandgaps that are
P. Ruffieux +13 more
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Canadian Journal of Mathematics, 1965
An H-space is a topological space T for which it is possible to define a continuous binary compositionwith the following properties: there exists a homotopy unit, i.e.
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An H-space is a topological space T for which it is possible to define a continuous binary compositionwith the following properties: there exists a homotopy unit, i.e.
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The Topology of Elliptic Surfaces
1994In this chapter, we shall complete the classical (i.e., pre-gauge theory) analysis of the C ∞-topology of elliptic surfaces. In particular we shall compare deformation equivalence and diffeomorphism in all cases except when the fundamental group of the elliptic surface is finite cyclic.
John W. Morgan, Robert Friedman
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The surface and the abyss/Rethinking topology
Environment and Planning D: Society and Space, 2015Through a critical deployment of the surface/depth metaphor, this article explores the catalytic potential of topological thinking to establish points of articulation between apparently opposed notions and canons of thought. Starting from a genealogy of mathematical developments and philosophical mediations toward the end point of geography, we ...
Lata I. B., Minca C.
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