Relevant bibliographies by topics / Semialgebraic and subanalytic geometry

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  1. Journal articles

Academic literature on the topic 'Semialgebraic and subanalytic geometry'

Author: Grafiati
Published: 1 September 2023

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Journal articles on the topic "Semialgebraic and subanalytic geometry"

1

Coste, Michel. "Book Review: Geometry of subanalytic and semialgebraic sets." Bulletin of the American Mathematical Society 36, no. 04 (1999): 523–28. http://dx.doi.org/10.1090/s0273-0979-99-00793-4.

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2

Loi, Ta Lê. "Transversality theorem in o-minimal structures." Compositio Mathematica 144, no. 5 (2008): 1227–34. http://dx.doi.org/10.1112/s0010437x08003503.

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AbstractIn this paper we present Thom’s transversality theorem in o-minimal structures (a generalization of semialgebraic and subanalytic geometry). There are no restrictions on the differentiability class and the dimensions of manifolds involved in comparison withthe general case.
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3

Figueiredo, Rodrigo. "O-minimal de Rham Cohomology." Bulletin of Symbolic Logic 28, no. 4 (2022): 529. http://dx.doi.org/10.1017/bsl.2021.20.

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AbstractO-minimal geometry generalizes both semialgebraic and subanalytic geometries, and has been very successful in solving special cases of some problems in arithmetic geometry, such as André–Oort conjecture. Among the many tools developed in an o-minimal setting are cohomology theories for abstract-definable continuous manifolds such as singular cohomology, sheaf cohomology and Čech cohomology, which have been used for instance to prove Pillay’s conjecture concerning definably compact groups. In the present thesis we elaborate an o-minimal de Rham cohomology theory for abstract-definable $C^{\infty }$ manifolds in an o-minimal expansion of the real field which admits smooth cell decomposition and defines the exponential function. We can specify the o-minimal cohomology groups and attain some properties such as the existence of Mayer–Vietoris sequence and the invariance under abstract-definable $C^{\infty }$ diffeomorphisms. However, in order to obtain the invariance of our o-minimal cohomology under abstract-definable homotopy we must work in a tame context that defines sufficiently many primitives and assume the validity of a statement related to Bröcker’s question.Abstract prepared by Rodrigo Figueiredo.E-mail: rodrigo@ime.usp.brURL: https://doi.org/10.11606/T.45.2019.tde-28042019-181150
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4

KOVACSICS, PABLO CUBIDES, and KIEN HUU NGUYEN. "A P-MINIMAL STRUCTURE WITHOUT DEFINABLE SKOLEM FUNCTIONS." Journal of Symbolic Logic 82, no. 2 (2017): 778–86. http://dx.doi.org/10.1017/jsl.2016.58.

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AbstractWe show there are intermediate P-minimal structures between the semialgebraic and subanalytic languages which do not have definable Skolem functions. As a consequence, by a result of Mourgues, this shows there are P-minimal structures which do not admit classical cell decomposition.
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5

Kaiser, Tobias. "Capacity in subanalytic geometry." Illinois Journal of Mathematics 49, no. 3 (2005): 719–36. http://dx.doi.org/10.1215/ijm/1258138216.

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6

Niederman, Laurent. "Hamiltonian stability and subanalytic geometry." Annales de l’institut Fourier 56, no. 3 (2006): 795–813. http://dx.doi.org/10.5802/aif.2200.

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7

Zeng, Guangxin. "Homogeneous Stellensätze in semialgebraic geometry." Pacific Journal of Mathematics 136, no. 1 (1989): 103–22. http://dx.doi.org/10.2140/pjm.1989.136.103.

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8

Łojasiewicz, Stanisław. "On semi-analytic and subanalytic geometry." Banach Center Publications 34, no. 1 (1995): 89–104. http://dx.doi.org/10.4064/-34-1-89-104.

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9

Qi, Yang, Pierre Comon, and Lek-Heng Lim. "Semialgebraic Geometry of Nonnegative Tensor Rank." SIAM Journal on Matrix Analysis and Applications 37, no. 4 (2016): 1556–80. http://dx.doi.org/10.1137/16m1063708.

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10

Solernó, Pablo. "Effective Łojasiewicz inequalities in semialgebraic geometry." Applicable Algebra in Engineering, Communication and Computing 2, no. 1 (1991): 1–14. http://dx.doi.org/10.1007/bf01810850.

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