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Euler Classes of Combinatorial Manifolds

Published online by Cambridge University Press:  20 November 2018

Michael A. Penna
Michael A. Penna*
Affiliation:
Indiana University—Purdue University at Indianapolis, Indianapolis, Indiana
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Every finite simplicial complex has a tangent bundle in the category of simplicial bundles (see [9]). The goal of this paper is to classify simplicial bundles, and, as an application of this result, to construct Euler classes for a large class of combinatorial manifolds. This construction is closely related to [3] and [4].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 4 , April 1980 , pp. 783 - 803
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Banchoff, T., Critical points and curvature for embedded polyhedra, J. Differential Geometry 1 (1967), 245–256.Google Scholar
2. Cairns, S., Triangulated manifolds which are not Brouwer manifolds, Annals of Math. 41 (1940), 792–795.Google Scholar
3. Gabrielov, A. M., Gelfand, I. M., and Losik, M. V., Combinatorial computation of characteristic classes, Functional Analysis and its Applications 9 (1975), 186–202.Google Scholar
4. Gabrielov, A. M., Gelfand, I. M., and Losik, M. V., Combinatorial calculus of characteristic classes, Functional Analysis and its Applications 9 (1975), 103–115.Google Scholar
5. Husemoller, D., Fiber bundles (McGraw-Hill, 1966).CrossRefGoogle Scholar
6. MacPherson, R., The combinatorial formula of Gabrielov, Gelfand, and Losik for the first Pontrjagin class, Seminaire Bourbaki 29e année (1976/1977) No. 497, 1–19.Google Scholar
7. Maunder, C. R. F., Algebraic topology (Van Nostrand Reinhold Co., 1970).Google Scholar
8. Penna, M., Differential geometry on simplicial spaces, Transactions of the A.M.S. 214 (1975), 303–323.Google Scholar
9. Penna, M., Vector fields on polyhedra, Transactions of the A. M.S. 232 (1977), 1–31.Google Scholar
10. Penna, M., On the geometry of combinatorial manifolds, Pacific J. of Math. 76 (1978), 50–74.Google Scholar
11. Spivak, M., A comprehensive introduction to differenial geometry, Publish or Perish, (1975).Google Scholar