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- W2804101841 abstract "In this work, we present a brief survey of knot theory supported by contact 3-manifolds. We focus on transverse knots and explore different ways of studying transverse knots. We define a new family of transverse invariants, this is accomplished by considering $n$-fold cyclic branched covers branched along a transverse knot and we then extend the definition of the BRAID invariant $t$ defined in cite{BVV} to the lift of the transverse knot. We call the new invariant the lift of the BRAID invariant and denote it by $t_n$. We then go on to show that $t_n$ satisfies a comultiplication formula and use this result to prove a vanishing theorem for $t_n$. We also re-prove a previously known result regarding the $n$-fold branched covers branched along stabilized transverse knot. We use this result to prove another vanishing result for $t_n$." @default.
- W2804101841 created "2018-06-01" @default.
- W2804101841 creator A5029176347 @default.
- W2804101841 date "2022-06-10" @default.
- W2804101841 modified "2023-10-15" @default.
- W2804101841 title "On Braids, Branched Covers and Transverse Invariants" @default.
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- W2804101841 doi "https://doi.org/10.31390/gradschool_dissertations.4211" @default.
- W2804101841 hasPublicationYear "2022" @default.
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