Nicolas Dutertre

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Documents

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Publications

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LÊ-GREUEL TYPE FORMULAS FOR SOME MAPPINGS FROM (R^n,0) TO (R^2,0)

Nicolas Dutertre , Juan Antonio Moya Pérez

Research in the Mathematical Sciences , 2025, 12 (4), pp.92. ⟨10.1007/s40687-025-00579-7⟩

Article dans une revue hal-05303558v1
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EQUI-SINGULARITY OF REAL FAMILIES AND LIPSCHITZ KILLING CURVATURE DENSITIES AT INFINITY

Nicolas Dutertre , Vincent Grandjean

Annales de l'Institut Fourier, 2024, pp.2379-2423. ⟨10.5802/aif.3607⟩

Article dans une revue hal-04213877v1
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PRINCIPAL KINEMATIC FORMULAS FOR GERMS OF CLOSED DEFINABLE SETS

Nicolas Dutertre

Advances in Mathematics, 2022, 399, ⟨10.1016/j.aim.2022.108251⟩

Article dans une revue hal-03089027v1
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Gauss-Kronecker Curvature and equisingularity at infinity of definable families

Nicolas Dutertre , Vincent Grandjean

Asian Journal of Mathematics, 2021, pp.815-840. ⟨10.4310/AJM.2021.v25.n6.a2⟩

Article dans une revue hal-02308350v1
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On the topology of non-isolated real singularities

Nicolas Dutertre

Journal of Singularities, 2020, Proc. of 15th International Workshop on Singularities, São Carlos, 2018, 22, pp.159-179. ⟨10.5427/jsing.2020.22j⟩

Article dans une revue hal-01985272v1
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Global Euler obstruction, global Brasselet numbers and critical points

Nicolas Dutertre , Nivaldo Grulha

Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2020, 150 (5), pp.2503-2534. ⟨10.1017/prm.2019.30⟩

Article dans une revue hal-02129140v1
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Lipschitz-Killing curvatures and polar images

Nicolas Dutertre

Advances in Geometry, 2019, 19 (2), pp.205-230. ⟨10.1515/advgeom-2018-0019⟩

Article dans une revue hal-01239927v1
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Topology of real Milnor fibration for non-isolated singularities

Nicolas Dutertre , Raimundo N. Araújo dos Santos

International Mathematics Research Notices, 2016, 2016 (16), pp.4849-4866. ⟨10.1093/imrn/rnv286⟩

Article dans une revue hal-00757428v1
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Open book structures on semi-algebraic manifolds

Nicolas Dutertre , Raimundo N. Araújo dos Santos , Ying Chen , Antonio Andrade

Manuscripta mathematica, 2016, 149 (1), pp.18. ⟨10.1007/s00229-015-0772-4⟩

Article dans une revue hal-01064170v2
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Fibrations structure and degree formulae for Milnor fibers

Nicolas Dutertre , Raimundo N. Araújo dos Santos , Ying Chen , Antonio Andrade

RIMS Kokyuroku Bessatsu, 2016, Theory of singularities of smooth mappings and around it B55, pp.41-65

Article dans une revue hal-01064938v1
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Euler obstruction and Lipschitz-Killing curvatures

Nicolas Dutertre

Israel Journal of Mathematics, 2016, 213, pp.109-137. ⟨10.1007/s11856-016-1322-9⟩

Article dans une revue hal-00995743v1
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Stratified critical points on the real Milnor fibre and integral-geometric formulas

Nicolas Dutertre

Journal of Singularities, 2015, 13, pp.20. ⟨10.5427/jsing.2015.13e⟩

Article dans une revue hal-00848992v1

Some notes on the Euler obstruction of a function

Nivaldo G. Grulha Jr. , Nicolas Dutertre

Journal of Singularities, 2014, 10, pp.82-91. ⟨10.5427/jsing.2014.10e⟩

Article dans une revue hal-01103220v1
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Lê-Greuel type formula for the Euler obstruction and applications

Nicolas Dutertre , Nivaldo G. Grulha Jr.

Advances in Mathematics, 2014, 251, pp.127-146

Article dans une revue hal-00626791v1
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On the topology of stable maps

Nicolas Dutertre , Toshizumi Fukui

Journal of the Mathematical Society of Japan, 2014, 66 (1), pp.161-203. ⟨10.2669/jmsj/06610161⟩

Article dans une revue hal-00516856v1

Degree formulas and signature formulas for the Euler characteristic of real algebraic sets

Nicolas Dutertre

Journal of Mathematical Sciences, 2013, 195 (2), pp.8. ⟨10.1007/s10958-013-1569-1⟩

Article dans une revue hal-01218134v1
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Euler characteristic and Lipschitz-Killing curvatures of closed semi-algebraic sets

Nicolas Dutertre

Geometriae Dedicata, 2012, 158 (1), pp.167-189

Article dans une revue hal-00453032v1
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On the topology of semi-algebraic functions on closed semi-algebraic sets

Nicolas Dutertre

Manuscripta mathematica, 2012, 139 (3-4), pp.415-441

Article dans une revue hal-00545183v1
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Radial index and Poincaré-Hopf index of 1-forms on semi-analytic sets

Nicolas Dutertre

Mathematical Proceedings of the Cambridge Philosophical Society, 2010, 148 (2), pp.297-330

Article dans une revue hal-00367729v1
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Semi-algebraic neighborhoods of closed semi-algebraic sets

Nicolas Dutertre

Annales de l'Institut Fourier, 2009, 59 (1), pp.429-458

Article dans une revue hal-00018914v1
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On the Euler characteristics of real Milnor fibres of partially parallelizable maps of $(\mathbb{R}^n,0)$ to $(\mathbb{R}^2,0)$

Nicolas Dutertre

Kodai Mathematical Journal, 2009, 32, pp.324-351

Article dans une revue hal-00203473v1
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A Gauss-Bonnet formula for closed semi-algebraic sets.

Nicolas Dutertre

Advances in Geometry, 2008, 8, pp.33-51

Article dans une revue hal-00077964v1

Topological formulas for closed semi-algebraic sets by Euler integration

Nicolas Dutertre , Juan Antonio Moya Pérez

XIII International Workshop Real and Complex Singularities, Jul 2014, Sao Carlos, Brazil. pp.89-102, ⟨10.1090/conm/675/13585⟩

Communication dans un congrès hal-01481958v1

Topology of the real Milnor fiber for isolated singularities

Raimundo N. Araújo dos Santos , Nicolas Dutertre , Daniel Dreibelbis

Real and Complex Singularities, XI International Workshop on Real and Complex Singularities, Jul 2010, ICMC, USP, Sao Carlos, Brazil. pp.9, ⟨10.1090/conm/569/11242⟩

Communication dans un congrès hal-01218152v1

Topology of Real Singularities

Nicolas Dutertre

Singularities and Foliations. Geometry, Topology and Applications. Brazil-Mexico Meeting on Singularities, Northeastern Brazilian Meeting on Singularities (2015)., 2018

Chapitre d'ouvrage hal-01777412v1

Topology and geometry of real singularities

Nicolas Dutertre

School on Real and Complex Singularities in Sao carlos, 2012, 2016

Chapitre d'ouvrage hal-01663143v1