Editing Topology (section)

=== Physics ===
Topology is relevant to physics in areas such as [[condensed matter physics]],<ref>{{cite web|title=The Nobel Prize in Physics 2016|url=https://www.nobelprize.org/nobel_prizes/physics/laureates/2016/press.html|publisher=Nobel Foundation|date=4 October 2016|access-date=12 October 2016|archive-date=6 October 2016|archive-url=https://web.archive.org/web/20161006230055/https://www.nobelprize.org/nobel_prizes/physics/laureates/2016/press.html|url-status=live}}</ref> [[quantum field theory]], [[quantum computing]] and [[physical cosmology]].

The topological dependence of mechanical properties in solids is of interest in the disciplines of [[mechanical engineering]] and [[materials science]]. Electrical and mechanical properties depend on the arrangement and network structures of [[molecules]] and elementary units in materials.<ref>{{cite journal|last1=Stephenson|first1=C.|last2=et.|first2=al.|title=Topological properties of a self-assembled electrical network via ab initio calculation|journal=Sci. Rep.|volume=7|pages=41621|date=2017|doi=10.1038/srep41621|pmid=28155863|pmc=5290745|bibcode=2017NatSR...741621S}}</ref> The [[compressive strength]] of [[Crumpling|crumpled]] topologies is studied in attempts to understand the high strength to weight of such structures that are mostly empty space.<ref>{{cite journal |last1=Cambou| first1=Anne Dominique |last2=Narayanan | first2=Menon| title=Three-dimensional structure of a sheet crumpled into a ball.| journal= Proceedings of the National Academy of Sciences of the United States of America |year=2011 | volume=108 |issue=36 |pages=14741–14745 | doi=10.1073/pnas.1019192108| pmid=21873249 |arxiv=1203.5826|bibcode=2011PNAS..10814741C|pmc=3169141| doi-access=free }}</ref> Topology is of further significance in [[Contact mechanics]] where the dependence of stiffness and friction on the [[Fractal dimension|dimensionality]] of surface structures is the subject of interest with applications in multi-body physics.

A [[topological quantum field theory]] (or topological field theory or TQFT) is a quantum field theory that computes [[topological invariant]]s. Although TQFTs were invented by physicists, they are also of mathematical interest, being related to, among other things, [[knot theory]], the theory of [[four-manifold]]s in algebraic topology, and the theory of [[moduli spaces]] in algebraic geometry. [[Simon Donaldson|Donaldson]], [[Vaughan Jones|Jones]], [[Edward Witten|Witten]], and [[Maxim Kontsevich|Kontsevich]] have all won [[Fields Medal]]s for work related to topological field theory.

The topological classification of [[Calabi–Yau manifold]]s has important implications in [[string theory]], as different manifolds can sustain different kinds of strings.<ref>Yau, S. & Nadis, S.; ''The Shape of Inner Space'', Basic Books, 2010.</ref>

In [[topological quantum computer]]s, the qubits are stored in [[topological properties]], that are by definition invariant with respect to [[homotopies]].<ref>{{cite journal |last=Kitaev |first=Alexei |date=9 July 1997 |title=Fault-tolerant quantum computation by anyons |journal= Annals of Physics|volume=303 |issue=1 |pages=2–30 |doi=10.1016/S0003-4916(02)00018-0 |arxiv=quant-ph/9707021v1|bibcode=2003AnPhy.303....2K |s2cid=11199664 }}</ref>

In cosmology, topology can be used to describe the overall [[shape of the universe]].<ref>''The Shape of Space: How to Visualize Surfaces and Three-dimensional Manifolds'' 2nd ed (Marcel Dekker, 1985, {{isbn|0-8247-7437-X}})</ref> This area of research is commonly known as [[spacetime topology]].

In condensed matter, a relevant application to topological physics comes from the possibility of obtaining a one-way current, which is a current protected from backscattering. It was first discovered in electronics with the famous [[quantum Hall effect]], and then generalized in other areas of physics, for instance in photonics<ref>{{Cite journal |last1=Haldane |first1=F. D. M. |last2=Raghu |first2=S. |date=2008-01-10 |title=Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry |url=https://link.aps.org/doi/10.1103/PhysRevLett.100.013904 |journal=Physical Review Letters |language=en |volume=100 |issue=1 |pages=013904 |doi=10.1103/PhysRevLett.100.013904 |pmid=18232766 |arxiv=cond-mat/0503588 |bibcode=2008PhRvL.100a3904H |s2cid=44745453 |issn=0031-9007}}</ref> by [[Duncan Haldane|F.D.M Haldane]].