Zobrazeno 1 - 10
of 104
pro vyhledávání: '"Dunfield, Nathan"'
Autor:
Dunfield, Nathan M., Tiozzo, Giulio
Motivated by an observation of Dehornoy, we study the roots of Alexander polynomials of knots and links that are closures of positive 3-strand braids. We give experimental data on random such braids and find that the roots exhibit marked patterns, wh
Externí odkaz:
http://arxiv.org/abs/2402.06771
Inspired by the notions of local equivalence in monopole and Heegaard Floer homology, we introduce a version of local equivalence that combines odd Khovanov homology with equivariant even Khovanov homology into an algebraic package called a local eve
Externí odkaz:
http://arxiv.org/abs/2312.09114
In earlier work of two of the authors, two 1-loop polynomial invariants of cusped 3-manifolds were constructed using combinatorial data of ideal triangulations, and conjectured to be equal to the $\mathbb{C}^2$ and the $\mathbb{C}^3$-torsion polynomi
Externí odkaz:
http://arxiv.org/abs/2304.00469
For a ribbon knot, it is a folk conjecture that the rank of its knot Floer homology must be 1 modulo 8, and another folk conjecture says the same about reduced Khovanov homology. We give the first counter-examples to both of these folk conjectures, b
Externí odkaz:
http://arxiv.org/abs/2303.04233
Autor:
Dunfield, Nathan M., Rasmussen, Jacob
We introduce a unified framework for counting representations of knot groups into $SU(2)$ and $SL(2, \mathbb{R})$. For a knot $K$ in the 3-sphere, Lin and others showed that a Casson-style count of $SU(2)$ representations with fixed meridional holono
Externí odkaz:
http://arxiv.org/abs/2209.03382
Publikováno v:
Proceedings of the 38th International Symposium on Computational Geometry (SoCG 2022), pages 37:1--37:24
A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the knot. Knots are typically encoded by planar diagram
Externí odkaz:
http://arxiv.org/abs/2112.03251
Autor:
Peddada, Satya R. T., Dunfield, Nathan M., Zeidner, Lawrence E., Givans, Zane R., James, Kai A., Allison, James T.
Publikováno v:
Journal of Mechanical Design, paper no. MD-22-1755, pages 1-34, 2023
Systematic enumeration and identification of unique 3D spatial topologies of complex engineering systems (such as automotive cooling systems, electric power trains, satellites, and aero-engines) are essential to navigation of these expansive design s
Externí odkaz:
http://arxiv.org/abs/2107.13724
We consider the natural problem of counting isotopy classes of essential surfaces in 3-manifolds, focusing on closed essential surfaces in a broad class of hyperbolic 3-manifolds. Our main result is that the count of (possibly disconnected) essential
Externí odkaz:
http://arxiv.org/abs/2007.10053
Autor:
Dunfield, Nathan M.
Publikováno v:
Geom. Topol. 24 (2020) 2075-2125
This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and admitting a co-orientable taut foliation. In particular, it
Externí odkaz:
http://arxiv.org/abs/1904.04628
Autor:
Dunfield, Nathan M.
This paper describes the complete list of all 205,822 exceptional Dehn fillings on the 1-cusped hyperbolic 3-manifolds that have ideal triangulations with at most 9 ideal tetrahedra. The data is consistent with the standard conjectures about Dehn fil
Externí odkaz:
http://arxiv.org/abs/1812.11940