Covering maps and fibrations of spaces fulfilling certain technical conditions are known to satisfy a multiplicative formula relating the Euler characteristic of the domain to that of the codomain. An open question posed by Albrecht Dold in 1980 asks in general when this is true and can be stated as: for which classes of maps is it true that if χ(X) denotes the Euler characteristic of a space X, and if f : X → Y has the property that the Euler characteristic of the preimage of y is k for all y ∈ Y and for some integer k, the multiplicative formula χ(X) = k · χ(Y ) holds? A corroborative answer is given herein for simplicial maps of finite simplicial complexes, while counterexamples are constructed for cellular maps of finite CW complexes, continuous maps of closed topological manifolds, and even smooth maps of smooth manifolds. / 1 / Kelley Brook Johnson
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_45941 |
| Date | January 2015 |
| Contributors | Johnson, Kelley B. (author), Kwasik, Slawomir (Thesis advisor), School of Science & Engineering Mathematics (Degree granting institution) |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | electronic |
| Rights | No embargo |
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