Abstract
Differential forms play a role in various realms of mathematics. Here, we work mainly from the perspective of algebraic topology, namely, we work with de Rham cohomology.
We discuss the Poincaré Lemma, the Brouwer Fixed-Point Theorem, the Jordan-Brouwer Separation Theorem, and the Stokes’s Integral Formula. There are numerous exercises concerning differential forms and cohomology.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Johann Friedrich Pfaff (1765–1825).
- 2.
Georges de Rham (1903–1990).
- 3.
Enrico Betti (1823–1892).
- 4.
Walther Mayer (1887–1948), Leopold Vietoris (1891–2002).
- 5.
Luitzen Egbertus Jan Brouwer (1881–1966).
- 6.
Henri Léon Lebesgue (1875–1941).
- 7.
Sir George Gabriel Stokes (1819–1903).
- 8.
Guido Fubini (1879–1943).
References
I. Agricola, T. Friedrich, Global Analysis. Differential Forms in Analysis, Geometry and Physics. Graduate Studies in Mathematics, vol. 52 (American Mathematical Society, Providence, 2008), xii+243 pp. Translated from the German by Andreas Nestke
R. Bott, L. Tu, Differential Forms in Algebraic Topology. Graduate Texts in Mathematics, vol. 82 (Springer, Berlin, 1982), xiv+331 pp.
S. Lang, Real Analysis (Addison-Wesley, Reading, 1969), xi+476 pp.
I.M. Singer, J.A. Thorpe, Lecture Notes on Elementary Topology and Geometry, Reprint of the 1967 edition. Undergraduate Texts in Mathematics (Springer, Berlin, 1976), viii+232 pp.
M. Spivak, A Comprehensive Introduction to Differential Geometry. Vol. I, 2nd edn. (Publish or Perish, Berkeley, 1979), xiv+668 pp.
H. Whitney, Geometric Integration Theory (Princeton University Press, Princeton, 1957), xv+387 pp.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Basel
About this chapter
Cite this chapter
Ballmann, W. (2018). Differential Forms and Cohomology. In: Introduction to Geometry and Topology. Compact Textbooks in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0983-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-0348-0983-2_3
Published:
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-0982-5
Online ISBN: 978-3-0348-0983-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)