Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Marc Kegel"'
Autor:
Chris Anderson, Kenneth L. Baker, Xinghua Gao, Marc Kegel, Khanh Le, Kyle Miller, Sinem Onaran, Geoffrey Sangston, Samuel Tripp, Adam Wood, Ana Wright
Publikováno v:
Experimental Mathematics. :1-15
In Dunfield's catalog of the hyperbolic manifolds in the SnapPy census which are complements of L-space knots in $S^3$, we determine that $22$ have tunnel number $2$ while the remaining all have tunnel number $1$. Notably, these $22$ manifolds contai
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e75fcad4205416a1e103590e159df3ef
https://doi.org/10.1080/10586458.2021.1980753
https://doi.org/10.1080/10586458.2021.1980753
Autor:
Sinem Onaran, Marc Kegel
We define a graph encoding the structure of contact surgery on contact 3-manifolds and analyze its basic properties and some of its interesting subgraphs.
11 pages, 3 figures
11 pages, 3 figures
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::58ba029d34f0bb4338fe064e2bab7bbf
http://arxiv.org/abs/2201.03505
http://arxiv.org/abs/2201.03505
We present a simple proof of the surface classification theorem using normal curves. This proof is analogous to Kneser's and Milnor's proof of the existence and uniqueness of the prime decomposition of 3-manifolds. In particular, we do not need any i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5927281b7d2bce1d81268f9565c7c746
Publikováno v:
Michigan Mathematical Journal. 70
This paper introduces techniques for computing a variety of numerical invariants associated to a Legendrian knot in a contact manifold presented by an open book with a Morse structure. Such a Legendrian knot admits a front projection to the boundary
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::02b0b4004bcb5ae4de15ece84816a916
https://doi.org/10.1307/mmj/20195780
https://doi.org/10.1307/mmj/20195780
Autor:
Christian Lange, Marc Kegel
A Reeb flow on a contact manifold is called Besse if all its orbits are periodic, possibly with different periods. We characterize contact manifolds whose Reeb flows are Besse as principal $$S^1$$ S 1 -orbibundles over integral symplectic orbifolds s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::87683b2970e729c2f9c93c76f488acdd
Autor:
Marc Kegel, Sebastian Durst
Publikováno v:
Acta Mathematica Hungarica. 150:524-540
We give an explicit formula to compute the rotation number of a nullhomologous Legendrian knot in contact (1/n)-surgery diagrams along Legendrian links and obtain a corresponding result for the self-linking number of transverse knots. Moreover, we ex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1cdc3652293ae7def7a6b2067ad23c4b
https://doi.org/10.1007/s10474-016-0660-8
https://doi.org/10.1007/s10474-016-0660-8
We present two proofs that all closed, orientable 3-manifolds are parallelisable. Both are based on the Lickorish-Wallace surgery presentation; one proof uses a refinement due to Kaplan and some basic contact geometry. This complements a recent paper
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::55a8ecc83d6e54ace972e92ca653be8d
http://arxiv.org/abs/1808.05072
http://arxiv.org/abs/1808.05072
Given a knot in a closed connected orientable 3-manifold we prove that if the exterior of the knot admits an aperiodic contact form that is Euclidean near the boundary, then the 3-manifold is diffeomorphic to the 3-sphere and the knot is the unknot.<
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5b23f2149312c01ad0ae1e20cf7c7ace
http://arxiv.org/abs/1806.08603
http://arxiv.org/abs/1806.08603
We give an entirely geometric proof, without recourse to cellular homology, of the fact that $\partial^2=0$ in the chain complex defined by a handle decomposition of a given manifold. Topological invariance of the resulting `handle homology' is a con
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::40ba48bfb898d921a76a52095e9fefb5
Autor:
Marc Kegel
We study cosmetic contact surgeries along transverse knots in the standard contact 3-sphere, i.e. contact surgeries that yield again the standard contact 3-sphere. The main result is that we can exclude non-trivial cosmetic contact surgeries along al
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7c18f967ee34380ab971f2bae5cba153