Reduction cohomology of Riemann surfaces
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00575120" target="_blank" >RIV/67985840:_____/23:00575120 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1142/S0129055X23300054" target="_blank" >https://doi.org/10.1142/S0129055X23300054</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0129055X23300054" target="_blank" >10.1142/S0129055X23300054</a>
Alternative languages
Result language
angličtina
Original language name
Reduction cohomology of Riemann surfaces
Original language description
We study the algebraic conditions leading to the chain property of complexes for vertex operator algebra n-point functions (with their convergence assumed) with differential being defined through reduction formulas. The notion of the reduction cohomology of Riemann surfaces is introduced. Algebraic, geometrical, and cohomological meanings of reduction formulas are clarified. A counterpart of the Bott-Segal theorem for Riemann surfaces in terms of the reductions cohomology is proven. It is shown that the reduction cohomology is given by the cohomology of n-point connections over the vertex operator algebra bundle defined on a genus g Riemann surface S-(g). The reduction cohomology for a vertex operator algebra with formal parameters identified with local coordinates around marked points on S-(g) is found in terms of the space of analytical continuations of solutions to Knizhnik-Zamolodchikov equations. For the reduction cohomology, the Euler-Poincare formula is derived. Examples for various genera and vertex operator cluster algebras are provided.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Reviews in Mathematical Physics
ISSN
0129-055X
e-ISSN
1793-6659
Volume of the periodical
35
Issue of the periodical within the volume
7
Country of publishing house
SG - SINGAPORE
Number of pages
32
Pages from-to
2330005
UT code for WoS article
000990052000001
EID of the result in the Scopus database
2-s2.0-85171766528