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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)
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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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Linking options:
http://mi.mathnet.ru/eng/umn9357https://doi.org/10.4213/rm9357 http://mi.mathnet.ru/eng/umn/v65/i3/p5
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This publication is cited in the following articles:
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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
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Y. Baryshnikov, R. Ghrist, M. Wright, “Hadwiger's Theorem for definable functions”, Adv. Math., 245 (2013), 573–586
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R. Ehrenborg, M. Readdy, “Manifold arrangements”, J. Combin. Theory Ser. A, 125 (2014), 214–239
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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
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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
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Campillo A., Delgado F., Gusein-Zade S.M., “on Poincaré Series of Filtrations”, 5, no. 2, 2015, 125–139
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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
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S. M. Gusein-Zade, “Equivariant analogues of the Euler characteristic and Macdonald type equations”, Russian Math. Surveys, 72:1 (2017), 1–32
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Menegon Neto A., Seade J., “On the Lê-Milnor fibration for real analytic maps”, Math. Nachr., 290:2-3 (2017), 382–392
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