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19 April 2024 |
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A number theoretic result for Berge's conjecture | | Sarah Dean Rasmussen
; | | Date: |
13 Jan 2016 | | Abstract: | (Original version of PhD thesis, submitted in Spring 2009 to Harvard
University. Provides a solution of the $p > k^2$ case, corresponding to Berge
families I-VI, of the "Lens space realization problem" later solved in entirety
by Greene.) In the 1980’s, Berge proved that a certain collection of knots in
$S^3$ admitted lens space surgeries, a list which Gordon conjectured was
exhaustive. More recently, J. Rasmussen used techniques from Heegaard Floer
homology to translate the related problem of classifying simple knots in lens
spaces admitting L-space homology sphere surgeries into a combinatorial number
theory question about the data $(p,q,k)$ associated to a knot of homology class
$k in H_1(L(p,q))$ in the lens space $L(p,q)$. In the following paper, we
solve this number theoretic problem in the case of $p > k^2$. | | Source: | arXiv, 1601.3430 | | Services: | Forum | Review | PDF | Favorites | |
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