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Mat. Zametki:

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Mat. Zametki, 2002, Volume 72, Issue 2, Pages 236–257 (Mi mz418)  

This article is cited in 18 scientific papers (total in 18 papers)

Analysis on Loop Spaces and Topology

R. Léandre

Université Henri Poincaré — Nancy I

Abstract: Results on analysis on loop spaces and topologies are surveyed. In particular, Sobolev cohomology of loop spaces, stochastic Chen–Souriau cohomology, and Witten genus are described.


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English version:
Mathematical Notes, 2002, 72:2, 212–229

Bibliographic databases:

UDC: 517
Received: 09.02.2000

Citation: R. Léandre, “Analysis on Loop Spaces and Topology”, Mat. Zametki, 72:2 (2002), 236–257; Math. Notes, 72:2 (2002), 212–229

Citation in format AMSBIB
\by R.~L\'eandre
\paper Analysis on Loop Spaces and Topology
\jour Mat. Zametki
\yr 2002
\vol 72
\issue 2
\pages 236--257
\jour Math. Notes
\yr 2002
\vol 72
\issue 2
\pages 212--229

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    This publication is cited in the following articles:
    1. Léandre R., “Stochastic algebraic de Rham complexes”, Acta Appl. Math., 79:3 (2003), 217–247  crossref  mathscinet  zmath  isi  scopus  scopus
    2. Léandre R., “Stochastic complex K-theories: Chern character and Bott periodicity”, Lett. Math. Phys., 64:3 (2003), 185–202  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Léandre R., “Brownian surfaces with boundary and Deligne cohomology”, Rep. Math. Phys., 52:3 (2003), 353–362  crossref  mathscinet  zmath  adsnasa  isi
    4. Léandre R., “Brownian cylinders and intersecting branes”, Rep. Math. Phys., 52:3 (2003), 363–372  crossref  mathscinet  zmath  adsnasa  isi
    5. Léandre R., “Stochastic processes on classifying spaces and string structures”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 7:3 (2004), 361–381  crossref  mathscinet  zmath  isi  scopus  scopus
    6. Leandre R., “Bundle Gerbes and Brownian Motion”, Lie Theory and its Applications in Physics V, Proceedings, eds. Doebner H., Dobrev V., World Scientific Publ Co Pte Ltd, 2004, 342–352  crossref  mathscinet  isi
    7. Leandre R., “Malliavin Calculus and Real Bott Periodicity”, Proceedings of the International Conference on Stochastic Analysis and Applications, eds. Albeverio S., BoutetDeMonvel A., Ouerdiane H., Springer, 2004, 37–51  crossref  mathscinet  isi
    8. Leandre R., “Hypoelliptic Diffusions and Cyclic Cohomology”, Seminar on Stochastic Analysis, Random Fields and Applications IV, Progress in Probability, 58, eds. Dalang R., Dozzi M., Russo F., Birkhauser Boston, 2004, 165–185  mathscinet  zmath  isi
    9. Leandre R., “Wiener Analysis and Cyclic Homology”, Stochastic Analysis and Mathematical Physics (SAMP/ANESTOC 2002), eds. Rebolledo R., Rezende J., Zambrini J., World Scientific Publ Co Pte Ltd, 2004, 115–127  crossref  mathscinet  isi
    10. Léandre R., “Stochastic Poisson-Sigma model”, Ann. Sc. Norm. Super. Pisa Cl. Sci., 4:4 (2005), 653–667  mathscinet  isi
    11. Léandre R., “Stochastic equivariant cohomologies and cyclic cohomology”, Ann. Probab., 33:4 (2005), 1544–1572  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Léandre R., “Brownian pants and Deligne cohomology”, J. Math. Phys., 46:3 (2005), 033503, 20 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    13. Léandre R., Rogers A., “Equivariant cohomology, Fock space and loop groups”, J. Phys. A, 39:38 (2006), 11929–11946  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    14. Brzeźniak Z., Léandre R., “Fellerian pants”, C. R. Math. Acad. Sci. Paris, 343:5 (2006), 333–338  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Eyink G. L., “Turbulent diffusion of lines and circulations”, Phys. Lett. A, 368:6 (2007), 486–490  crossref  adsnasa  isi  elib  scopus  scopus
    16. Elworthy K. D., Li Xue-Mei, “An $L^2$ theory for differential forms on path spaces. I”, J. Funct. Anal., 254:1 (2008), 196–245  crossref  mathscinet  zmath  isi  scopus  scopus
    17. Elworthy K.D., “Stochastic Flows and Geometric Analysis on Path Spaces”, Probabilistic Approach to Geometry, Advanced Studies in Pure Mathematics, 57, eds. Kotani M., Hino M., Kumagai T., Math Soc Japan, 2010, 61–78  mathscinet  zmath  isi
    18. Elworthy K.D., Yang Y., “The Vanishing of l-2 Harmonic One-Forms on Based Path Spaces”, J. Funct. Anal., 264:5 (2013), 1168–1196  crossref  mathscinet  zmath  isi  scopus  scopus
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