topology

I would like to know sufficient conditions under which the direct limit of topological spaces is locally "nice" (connected, path-connected, contractible), direct limit commutes with the ...

A uniform space $X$ is called totally bounded if given any entourage $V$ of $X$ there exist finitely many points $x_j\in X$ such that $X=\bigcup_jV[x_j]$; it is known that a uniform space is compact ...

vector bundle, 2-vector bundle, (∞,1)-vector bundle real, complex/holomorphic, quaternionic A sphere fiber bundle is a fiber bundle whose fibers are spheres of some dimension . Often, but not always, this is considered in homotopy theory or even in stable homotopy theory, hence for fibers which have the (stable) homotopy type of a sphere, in which case one speaks of spherical fibrations. See ther…

Swapping materials in its Majorana 2 chip boosted the effectiveness of quantum bits that rely on the math of topology to reduce errors, Microsoft says.

This is a follow-up from this question that turned out to have a negative answer. Suppose we have a space homeomorphic to an open book with a single page. We have a subspace $D$, homeomorphic to a ...

On anyons in fractional quantum Hall systems as potential hardware for topological quantum computing: On anyons in application to quantum computation: Proposing nanowire experiments potentially realizing Majorana zero modes: Co-predicting the fractional quantum anomalous Hall effect: On the adiabaticity of topological quantum computation by braiding of defect anyons: On topological quantum comput…

Given an elementary topos $\mathcal{E}$ for an object $X$, we have the Heyting algebra of its subobjects $Sub(X)$. If $\mathcal{E}$ is a Grothendieck topos, then $Sub(X)$ is complete. In any case (in ...

I'm very unexperimented regarding homotopy (I basically know the definition), but I thought I had a good intuition regarding it, as it is very visual. I however just discovered (and it absolutely ...

I am a mathematician specializing in the algebraic theory of topological quantum computation, and the related underlying fields of pure mathematics. In particular, I am enthusiastic about the use of category theory to illuminate concepts in condensed matter physics and error correcting codes.

This working paper introduces a novel, non-dual philosophical and mathematical architecture termed the Hrithik Framework. We challenge the unexamined foundations of Western mathematics-specically the reliance on an unbounded decimal real number line derived from human biological constraints (base-10 counting). Instead, we propose a bounded, bipolar discrete field restricted to the interval [−1,+…

International audience

nLab point of a locale Context Topology topology (point-set topology , point-free topology ) see also differential topology , algebraic topology , functional analysis and topological homotopy theory Introduction Basic concepts open subset , closed subset , neighbourhood topological space , locale base for the topology , neighbourhood base finer/coarser topology closure , interior , boundary separ…

Motivated bz this question and in similar spirit to this, I ask this question. In topology quotient is an essential concept to be able to construct many spaces, however when it comes to manifold ...

and rational homotopy theory (equivariant, stable, parametrized, equivariant & stable, parametrized & stable) The concept of the PL de Rham complex (Bousfield-Gugenheim 76, Sullivan 77) is a variant of that of the de Rham complex for smooth manifolds which applies to general topological spaces and simplicial sets. The terminology “PL” for “piecewise linear” seems to have been tacitly introduced i…

Let $p:E \to B$ a Serre fibration and a homotopy $H:X \times I \to B$ with the initialization $X \times 0 \mapsto \tilde{h}_0$. Let $\tilde{H}_1$ and $\tilde{H}_2$ two different lifts of $H$. Are ...

nLab paracompact locale Context Topology topology (point-set topology , point-free topology ) see also differential topology , algebraic topology , functional analysis and topological homotopy theory Introduction Basic concepts open subset , closed subset , neighbourhood topological space , locale base for the topology , neighbourhood base finer/coarser topology closure , interior , boundary sepa…

I’m an assistant professor of mathematics at the University of Nevada, Reno. My research lies on the interface between algebraic topology, geometry, and mathematical physics. I am particularly interested in the role that homotopy theoretic and higher categorical structures play in quantization. My Ph.D thesis was on higher symplectic geometry, and was supervised by John Baez. More information (cu…

Joost Nuiten is a postdoc in mathematics at Université de Montpellier Joost Nuiten did his PhD student in mathematics at Utrecht University with Ieke Moerdijk; his Master in mathematics and physics at Utrecht University with Urs Schreiber. On the Bohr topos formulation of local quantum field theory (AQFT): On the quantization of boundary local prequantum field theory by motivic quantization: On c…

model category, model -category Definitions Morphisms Universal constructions Refinements Producing new model structures Presentation of -categories Model structures for -groupoids on chain complexes/model structure on cosimplicial abelian groups related by the Dold-Kan correspondence for equivariant -groupoids for rational -groupoids for rational equivariant -groupoids for -groupoids for -groups…