Abstract
We will study the smooth and piecewise linear manifolds within a given homotopy equivalence class. In the first part we find an obstruction theory for deforming a homotopy equivalence between manifolds to a diffeomorphism or a piecewise linear homeomorphism. In the second part we analyze the piecewise linear case and characterize the obstructions in terms of a geometric property of the homotopy equivalence. In the third part we apply this analysis to the Hauptvermutung and complex projective space.
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© 1996 Springer Science+Business Media Dordrecht
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Sullivan, D.P. (1996). Triangulating and Smoothing Homotopy Equivalences and Homeomorphisms. Geometric Topology Seminar Notes. In: Ranicki, A.A. (eds) The Hauptvermutung Book. K-Monographs in Mathematics, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3343-4_3
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DOI: https://doi.org/10.1007/978-94-017-3343-4_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4735-9
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