Stratification of real analytic mappings and images
Integrity signals
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Every semianalytic set admits a semianalytic stratification, i.e. a stratification consisting of semianalytic strata only.
“Moreover, it can be shown [21,28] that every semianalytic set admits a semianalytic stratification, i.e., a stratification consisting of semianalytic strata only.”
From Representations of the Weyl Algebra in Quantum Geometry (2009) · cites this paper as [21]
Cites
(1988) · Elsevier eBooks · doi:10.1016/c2013-0-11200-7 · Cited by 5,131 · see citing works
Fédérer, H. (1996) · Classics in mathematics · doi:10.1007/978-3-642-62010-2 · Cited by 2,760 · see citing works
A New Decision Method for Elementary Algebra
Seidenberg, A. (1954) · Annals of Mathematics · doi:10.2307/1969640 · Cited by 541 · see citing works
Łojasiewicz, S. (1965) · Medical Entomology and Zoology · Cited by 515 · see citing works
Introduction to the Theory of Analytic Spaces
Narasimhan, R. (1966) · Lecture notes in mathematics · doi:10.1007/bfb0077071 · Cited by 412 · see citing works
Ensembles et morphismes stratifiés
Thom, R. (1969) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1969-12138-5 · Cited by 394 · see citing works
Triangulation of semi-analytic sets
Łojasiewicz, S. (1964) · French digital mathematics library (Numdam) · Cited by 365 · see citing works
Mather, J. N. (1973) · Dynamical Systems · doi:10.1016/b978-0-12-550350-1.50021-7 · Cited by 180 · see citing works
De Rham cohomology of an analytic space
Bloom, T., & Herrera, M. E. (1969) · Inventiones mathematicae · doi:10.1007/bf01425536 · Cited by 78 · see citing works
Topological properties of subanalytic sets
Hardt, R. (1975) · Transactions of the American Mathematical Society · doi:10.1090/s0002-9947-1975-0379882-8 · Cited by 77 · see citing works
Self-citationSimpliziale Zerlegung abz�hlbarer analytischer R�ume
Giesecke, B. (1964) · Mathematische Zeitschrift · doi:10.1007/bf01111199 · Cited by 68 · see citing works
Slicing and intersection theory for chains associated with real analytic varieties
Hardt, R. (1972) · Acta Mathematica · doi:10.1007/bf02392214 · Cited by 40 · see citing works
Self-citationIntegration on a semianalytic set
Herrera, M. E. (1966) · Bulletin de la Société mathématique de France · doi:10.24033/bsmf.1637 · Cited by 37 · see citing works
Homology theory for real analytic and semianalytic sets
Hardt, R. (1975) · French digital mathematics library (Numdam) · Cited by 21 · see citing works
Self-citationDe Rham theorems on semianalytic sets
Herrera, M. E. (1967) · Bulletin of the American Mathematical Society · doi:10.1090/s0002-9904-1967-11772-5 · Cited by 12 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Semianalytic and subanalytic sets
Bierstone, E., & Milman, P. D. (1988) · Publications Mathématiques de l'IHÉS · doi:10.1007/bf02699126 · Cited by 671 · see citing works
Representations of the Weyl Algebra in Quantum Geometry
Fleischhack, C. (2009) · Communications in Mathematical Physics · doi:10.1007/s00220-008-0593-3 · Cited by 183 · see citing works
- Authors
- Hardt, R. M.
- Affiliations
- University of Minnesota (US)
- Corresponding author
- Hardt, Robert M.
- Venue
- Inventiones Mathematicae
- Published
- 1975-06
- Volume
- 28
- Issue
- 2
- Pages
- 193-208
- ISSN
- 0020-9910 (ISSN-L)
- 1432-1297
- OpenAlex
- W2059300827
- Cited by
- 129
- References
- 15
- Citations by year
- 2026: 1 · 2025: 1 · 2024: 2 · 2022: 2 · 2021: 3 · 2020: 6 · 2019: 5 · 2018: 1 · 2017: 1 · 2016: 2 · 2015: 5 · 2014: 2 · 2013: 1 · 2012: 4
- FWCI
- 1.08
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Inventiones mathematicae (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic Geometry and Number Theory
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical and Theoretical Analysis
- Keywords
- stratification, Whitney stratification, analytic sets, singularities of mappings
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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