In
mathematics, chiral homology, introduced by
Alexander Beilinson
Alexander A. Beilinson (born 1957) is the David and Mary Winton Green University professor at the University of Chicago and works on mathematics. His research has spanned representation theory, algebraic geometry and mathematical physics. In 1 ...
and
Vladimir Drinfeld
Vladimir Gershonovich Drinfeld ( uk, Володи́мир Ге́ршонович Дрінфельд; russian: Влади́мир Ге́ршонович Дри́нфельд; born February 14, 1954), surname also romanized as Drinfel'd, is a renowne ...
, 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
Jacob Alexander Lurie (born December 7, 1977) is an American mathematician who is a professor at the Institute for Advanced Study. Lurie is a 2014 MacArthur Fellow.
Life
When he was a student in the Science, Mathematics, and Computer Science ...
'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 ...
s.
[
]
See also
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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 In algebra, a chiral Lie algebra is a D-module on a curve with a certain structure of Lie algebra. It is related to an \mathcal_2-algebra via the Riemann–Hilbert correspondence In mathematics, the term Riemann–Hilbert correspondence refers to t ...
*
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