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dc.contributor.advisorOzsváth, Peter-
dc.contributor.authorDatta, Amitesh-
dc.contributor.otherMathematics Department-
dc.description.abstractIn this thesis, we establish strong constraints on the kernel of the (reduced) Burau representation $\beta_4:B_4\to \text{GL}_3\left(\mathbb{Z}\left[q^{\pm 1}\right]\right)$ of the braid group $B_4$, addressing a conjecture originally posed in the 1930s. The strategy of the proof is a concrete interpretation of $\beta_4\left(\sigma\right)$ in terms of the Garside normal form for $\sigma\in B_4$. More specifically, if $\sigma$ is a positive braid in $B_4$ satisfying certain constraints, then we show that $\beta_4\left(\sigma\right)$ is not a diagonal matrix by considering a new decomposition of positive braids and combinatorially interpreting $\beta_4\left(\sigma\right)$ in terms of this decomposition.-
dc.publisherPrinceton, NJ : Princeton University-
dc.relation.isformatofThe Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: <a href=> </a>-
dc.titleOn the Burau representation of the braid group $B_4$-
dc.typeAcademic dissertations (Ph.D.)-
Appears in Collections:Mathematics

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