In
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
, chiral homology, introduced by
Alexander Beilinson and
Vladimir Drinfeld, is, in their words, "a “quantum” version of (the algebra of functions on) the space of global horizontal sections of an affine
-scheme (i.e., the space of global solutions of a system of non-linear differential equations)."
Jacob Lurie's topological chiral homology gives an analog for
manifold
In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a n ...
s.
[
]
See also
*
Ran space In mathematics, the Ran space (or Ran's space) of a topological space ''X'' is a topological space \operatorname(X) whose underlying set is the set of all nonempty finite subsets of ''X'': for a metric space ''X'' the topology is induced by the ...
*
Chiral Lie algebra
*
Factorization homology In algebraic topology and category theory, factorization homology is a variant of topological chiral homology, motivated by an application to topological quantum field theory and cobordism hypothesis
In mathematics, the cobordism hypothesis, due to ...
References
*{{cite book, last1=Beilinson, first1=Alexander, authorlink1=Alexander Beilinson, last2=Drinfeld, first2=Vladimir, authorlink2=Vladimir Drinfeld , title=Chiral algebras, date=2004, publisher=American Mathematical Society, isbn=0-8218-3528-9, chapter=Chapter 4, url=http://www.math.uchicago.edu/~mitya/langlands.html
Homological algebra