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Uspekhi Mat. Nauk, 2010, Volume 65, Issue 3(393), Pages 5–42 (Mi umn9357)  

This article is cited in 9 scientific papers (total in 9 papers)

Integration with respect to the Euler characteristic and its applications

S. M. Gusein-Zade

M. V. Lomonosov Moscow State University

Abstract: The notion of integration with respect to the Euler characteristic and its generalizations are discussed: integration over the infinite-dimensional spaces of arcs and functions, motivic integration. The author describes applications of these notions to the computation of monodromy zeta functions, Poincaré series of multi-index filtrations, generating series of classes of certain moduli spaces, and so on.
Bibliography: 70 titles.

Keywords: Euler characteristic, motivic integration.

DOI: https://doi.org/10.4213/rm9357

Full text: PDF file (874 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2010, 65:3, 399–432

Bibliographic databases:

UDC: 515.171.5+512.717
MSC: 11S40, 14B05, 32Sxx, 57Qxx
Received: 20.01.2010

Citation: S. M. Gusein-Zade, “Integration with respect to the Euler characteristic and its applications”, Uspekhi Mat. Nauk, 65:3(393) (2010), 5–42; Russian Math. Surveys, 65:3 (2010), 399–432

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Curry J., Ghrist R., Robinson M., “Euler calculus with applications to signals and sensing”, Advances in applied and computational topology, Proc. Sympos. Appl. Math., 70, ed. Zomorodian A., Amer. Math. Soc., Providence, RI, 2012, 75–145  crossref  mathscinet  zmath  isi
    2. Y. Baryshnikov, R. Ghrist, M. Wright, “Hadwiger's Theorem for definable functions”, Adv. Math., 245 (2013), 573–586  crossref  mathscinet  zmath  isi  scopus
    3. R. Ehrenborg, M. Readdy, “Manifold arrangements”, J. Combin. Theory Ser. A, 125 (2014), 214–239  crossref  mathscinet  zmath  isi  scopus
    4. S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “On an equivariant version of the zeta function of a transformation”, Arnold Math. J., 1:2 (2015), 127–140  crossref  mathscinet  zmath  scopus
    5. Gusein-Zade S.M., Luengo I., Melle-Hernandez A., “Higher-Order Orbifold Euler Characteristics For Compact Lie Group Actions”, 145, no. 6, 2015, 1215–1222  crossref  mathscinet  zmath  isi  scopus
    6. Campillo A., Delgado F., Gusein-Zade S.M., “on Poincaré Series of Filtrations”, 5, no. 2, 2015, 125–139  mathscinet  zmath  isi
    7. G. D. Solomadin, “Poincaré series of filtration associated with Newton diagram and topological types of singularities”, Moscow University Mathematics Bulletin, 70:4 (2015), 171–175  mathnet  crossref  mathscinet
    8. S. M. Gusein-Zade, “Equivariant analogues of the Euler characteristic and Macdonald type equations”, Russian Math. Surveys, 72:1 (2017), 1–32  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    9. Menegon Neto A., Seade J., “On the Lê-Milnor fibration for real analytic maps”, Math. Nachr., 290:2-3 (2017), 382–392  crossref  mathscinet  zmath  isi  scopus
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