Stable classification of homotopy equivalences of fake lens spaces

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Title 
Stable classification of homotopy equivalences of fake lens spaces 
Author 
Nischal, Atul 
School 
Tulane University 
Academic Field 
Mathematics 
Abstract 
Stable classification of homotopy equivalences between two manifolds deals with the following question: If $f : M \to N$ is a homotopy equivalence between two manifolds, when is $f \times id\sb{\IR\sp{k}} : M \times \IR\sp{k} \to N \times \IR\sp{k}$ homotopic to a homeomorphism? Due to Mazur's result, we know that this is true as long as $k \ge\ {\rm dim} M + 2$ and f is tangential. Therefore, we try to minimize the value of k by imposing additional conditions. It is already known that if for each Sylow subgroup H of $\pi\sb1 M,$ where $\pi\sb1 M$ is finite, and the liftings $f\sb{H} : M\sb{H}\to N\sb{H}$ are homotopic to a homeomorphism, then $f\times id\sb{\IR\sp3} : M\times \IR\sp3 \to N \times \IR\sp3$ is homotopic to a homeomorphism. The next step would be to ask if under some additional conditions it is possible to obtain stabilization of f on multiplication by $\IR\sp2$. This turns out to be the most intricate case and this dissertation is devoted to its analysis The central ideas for the proof come from the inductive detection phenomenon and surgery theory of compact and noncompact manifolds. Heavy use of computational results for Lgroups of cyclic groups of order $p,\ \doubz\sb{p},$ as well as analysis of the surgery exact sequence are required at several stages 
Language 
eng 
Advisor(s) 
Kwasik, Slawomir 
Degree Date 
1997 
Degree 
Ph.D 
Publisher 
Tulane University 
Publication Date 
1997 
Source 
Source: 32 p., Dissertation Abstracts International, Volume: 5812, Section: B, page: 6614 
Identifier 
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Rights 
Copyright is in accordance with U.S. Copyright law 
Contact Information 
acase@tulane.edu 
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