In
deformation theory
In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution ''P'' of a problem to slightly different solutions ''P''ε, where ε is a small number, or a vector of small quantities. The infinitesima ...
, a branch of mathematics, Deligne's conjecture is about the
operadic structure on
Hochschild cochain complex. Various proofs have been suggested by
Dmitry Tamarkin,
Alexander A. Voronov,
James E. McClure and
Jeffrey H. Smith,
Maxim Kontsevich
Maxim Lvovich Kontsevich (, ; born 25 August 1964) is a Russian and French mathematician and mathematical physicist. He is a professor at the Institut des Hautes Études Scientifiques and a distinguished professor at the University of Miami. He ...
and
Yan Soibelman, and others, after an initial input of construction of homotopy algebraic structures on the Hochschild complex.
It is of importance in relation with
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and intera ...
.
See also
*
Piecewise algebraic space
References
{{reflist
Further reading
* https://ncatlab.org/nlab/show/Deligne+conjecture
* https://mathoverflow.net/questions/374/delignes-conjecture-the-little-discs-operad-one
Algebraic topology
String theory
Conjectures