Geometric Integration Theory
Abstract
A complete theory of integration as it appears in geometric and physical problems must include integration over oriented r-dimensional domains in n-space; both the integrand and the domain may be variable. This is the primary subject matter of the present book, designed to bring out the underlying geometric and analytic ideas and to give clear and complete proofs of the basic theorems. Originally published in 1957. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Integrity signals
Registry
Cites
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Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Every manifold can be triangulized, i.e. is isomorphic to some union of open simplices; this was originally known for nonanalytic manifolds and later extended to semianalytic sets in analytic manifolds.
“The deeper reason behind the investigation of simplices above is the fact that every manifold can be triangulized; this means, roughly speaking, it is isomorphic to some union of (open) simplices.”
From Representations of the Weyl Algebra in Quantum Geometry (2009) · cites this paper as [38]
Cited by
Sorted by citations
Infinitesimal computations in topology
Sullivan, D. (1977) · Publications mathématiques de l IHÉS · doi:10.1007/bf02684341 · Cited by 1,421 · 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
- Whitney, H.
- Corresponding author
- Whitney, Hassler
- Venue
- Princeton University Press eBooks
- Publisher
- Princeton University Press
- Published
- 1957-12-31
- OpenAlex
- W1522382323
- Cited by
- 1,391
- References
- 0
- Citations by year
- 2026: 13 · 2025: 14 · 2024: 30 · 2023: 39 · 2022: 31 · 2021: 36 · 2020: 53 · 2019: 47 · 2018: 60 · 2017: 36 · 2016: 56 · 2015: 53 · 2014: 35 · 2013: 47 · 2012: 55
- FWCI
- 13.57
- Type
- book
- Language
- en
- Open access
- closed
- Locations
- Princeton University Press eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical and Theoretical Analysis
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Advanced Differential Geometry Research
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- variable domains, differential forms
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.
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