Izvestiya: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izvestiya: Mathematics, 2017, Volume 81, Issue 2, Pages 329–358
DOI: https://doi.org/10.1070/IM8435
(Mi im8435)
 

On the product of cocycles in a polyhedral complex

B. Ya. Kazarnovskii

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
References:
Abstract: We construct an algorithm for multiplying cochains in a polyhedral complex. It depends on the choice of a linear functional on the ambient space. The cocycles form a subring in the ring of cochains, the coboundaries form an ideal in the ring of cocycles, and the quotient ring is the cohomology ring. The multiplication algorithm depends on the geometry of the cells of the complex. For simplicial complexes (the simplest geometry of cells), it reduces to the well-known Čech algorithm. Our algorithm is of geometric origin. For example, it applies in the calculation of mixed volumes of polyhedra and the construction of stable intersections of tropical varieties. In geometry it is customary to multiply cocycles with values in the exterior algebra of the ambient space. Therefore we assume that the ring of values is supercommutative.
Keywords: product of cocycles, polyhedral complex, polyhedron, tropical variety.
Funding agency Grant number
Russian Science Foundation 14-50-00150
This work was supported by the Russian Science Foundation (grant no. 14-50-00150) and carried out in the Institute of Information Transmission Problems (Kharkevich Institute) of the Russian Academy of Sciences.
Received: 31.07.2015
Bibliographic databases:
UDC: 514+515.14
Language: English
Original paper language: Russian
Citation: B. Ya. Kazarnovskii, “On the product of cocycles in a polyhedral complex”, Izv. Math., 81:2 (2017), 329–358
Citation in format AMSBIB
\Bibitem{Kaz17}
\by B.~Ya.~Kazarnovskii
\paper On the product of cocycles in a~polyhedral complex
\jour Izv. Math.
\yr 2017
\vol 81
\issue 2
\pages 329--358
\mathnet{http://mi.mathnet.ru//eng/im8435}
\crossref{https://doi.org/10.1070/IM8435}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3629024}
\zmath{https://zbmath.org/?q=an:1421.55005}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2017IzMat..81..329K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000401127400004}
\elib{https://elibrary.ru/item.asp?id=28931378}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85019738639}
Linking options:
  • https://www.mathnet.ru/eng/im8435
  • https://doi.org/10.1070/IM8435
  • https://www.mathnet.ru/eng/im/v81/i2/p97
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:410
    Russian version PDF:50
    English version PDF:14
    References:60
    First page:26
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024