Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Nerve complex
open-in-new
<p>In <a href="/facts/Topology/2EqW47cU">topology</a>, the nerve complex of a <a href="/facts/Set_family/WbYof7lP">set family</a> is an <a href="/facts/Abstract_simplicial_complex/ytwxClsf">abstract complex</a> that records the pattern of intersections between the sets in the family. It was introduced by <a href="/facts/Pavel_Alexandrov/booz6U09">Pavel Alexandrov</a> and now has many variants and generalisations, among them the Čech nerve of a cover, which in turn is generalised by <a href="/facts/Hypercovering/zSvm5JzP">hypercoverings</a>. It captures many of the interesting topological properties in an algorithmic or combinatorial way. </p>