scholarly journals Universal Bounds for Genus One Seifert Surfaces for Hyperbolic Knots and Surgeries with Non-Trivial JSJT-Decompositions

2003 ◽  
Vol 9 (1) ◽  
pp. 53-60 ◽  
Author(s):  
Yukihiro TSUTSUMI
2008 ◽  
Vol 17 (02) ◽  
pp. 141-155
Author(s):  
YUKIHIRO TSUTSUMI

It is known that free genus one knots do not admit Seifert surfaces with hyperbolic exteriors. In this paper, for any integer g ≥ 2, we exhibit a knot of genus g which bounds a minimal genus Seifert surface with hyperbolic exterior and a minimal genus free Seifert surface.


Author(s):  
Tiago Nardi ◽  
Emanuela Olivieri ◽  
Edward Kariuki ◽  
Davide Sassera ◽  
Michele Castelli

Abstract Ticks require bacterial symbionts for the provision of necessary compounds that are absent in their hematophagous diet. Such symbionts are frequently vertically transmitted and, most commonly, belong to the Coxiella genus, which also includes the human pathogen Coxiella burnetii. This genus can be divided in four main clades, presenting partial but incomplete co-cladogenesis with the tick hosts. Here we report the genome sequence of a novel Coxiella, endosymbiont of the African tick Amblyomma nuttalli, and the ensuing comparative analyses. Its size (~1 Mb) is intermediate between symbionts of Rhipicephalus species and other Amblyomma species. Phylogenetic analyses show that the novel sequence is the first genome of the B clade, the only one for which no genomes were previously available. Accordingly, it allows to draw an enhanced scenario of the evolution of the genus, one of parallel genome reduction of different endosymbiont lineages, which are now at different stages of reduction from a more versatile ancestor. Gene content comparison allows to infer that the ancestor could be reminiscent of Coxiella burnetii. Interestingly, the convergent loss of mismatch repair could have been a major driver of such reductive evolution. Predicted metabolic profiles are rather homogenous among Coxiella endosymbionts, in particular vitamin biosynthesis, consistently with a host-supportive role. Concurrently, similarities among Coxiella endosymbionts according to host genus and despite phylogenetic unrelatedness hint at possible host-dependent effects.


2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Arjan Dwarshuis ◽  
Majken Roelfszema ◽  
Jaap Top

AbstractThis note reformulates Mazur’s result on the possible orders of rational torsion points on elliptic curves over $$\mathbb {Q}$$ Q in a way that makes sense for arbitrary genus one curves, regardless whether or not the curve contains a rational point. The main result is that explicit examples are provided of ‘pointless’ genus one curves over $$\mathbb {Q}$$ Q corresponding to the torsion orders 7, 8, 9, 10, 12 (and hence, all possibilities) occurring in Mazur’s theorem. In fact three distinct methods are proposed for constructing such examples, each involving different in our opinion quite nice ideas from the arithmetic of elliptic curves or from algebraic geometry.


2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Eric D’Hoker ◽  
Carlos R. Mafra ◽  
Boris Pioline ◽  
Oliver Schlotterer

Abstract In an earlier paper, we constructed the genus-two amplitudes for five external massless states in Type II and Heterotic string theory, and showed that the α′ expansion of the Type II amplitude reproduces the corresponding supergravity amplitude to leading order. In this paper, we analyze the effective interactions induced by Type IIB superstrings beyond supergravity, both for U(1)R-preserving amplitudes such as for five gravitons, and for U(1)R-violating amplitudes such as for one dilaton and four gravitons. At each order in α′, the coefficients of the effective interactions are given by integrals over moduli space of genus-two modular graph functions, generalizing those already encountered for four external massless states. To leading and sub-leading orders, the coefficients of the effective interactions D2ℛ5 and D4ℛ5 are found to match those of D4ℛ4 and D6ℛ4, respectively, as required by non-linear supersymmetry. To the next order, a D6ℛ5 effective interaction arises, which is independent of the supersymmetric completion of D8ℛ4, and already arose at genus one. A novel identity on genus-two modular graph functions, which we prove, ensures that up to order D6ℛ5, the five-point amplitudes require only a single new modular graph function in addition to those needed for the four-point amplitude. We check that the supergravity limit of U(1)R-violating amplitudes is free of UV divergences to this order, consistently with the known structure of divergences in Type IIB supergravity. Our results give strong consistency tests on the full five-point amplitude, and pave the way for understanding S-duality beyond the BPS-protected sector.


1988 ◽  
Vol 20 (1) ◽  
pp. 61-64 ◽  
Author(s):  
Martin Scharlemann ◽  
Abigail Thompson
Keyword(s):  

2019 ◽  
Vol 2019 (749) ◽  
pp. 65-86
Author(s):  
Pete L. Clark ◽  
Allan Lacy

Abstract We show that a nontrivial abelian variety over a Hilbertian field in which the weak Mordell–Weil theorem holds admits infinitely many torsors with period any given n>1 that is not divisible by the characteristic. The corresponding statement with “period” replaced by “index” is plausible but open, and it seems much more challenging. We show that for every infinite, finitely generated field K, there is an elliptic curve E_{/K} which admits infinitely many torsors with index any given n>1 .


2001 ◽  
Vol 10 (05) ◽  
pp. 781-794 ◽  
Author(s):  
MASAKAZU TERAGAITO

In the present paper, we will study the creation of Klein bottles by Dehn surgery on knots in the 3-sphere, and we will give an upper bound for slopes creating Klein bottles for non-cabled knots by using the genera of knots. In particular, it is shown that if a Klein bottle is created by Dehn surgery on a genus one knot then the knot is a doubled knot. As a corollary, we obtain that genus one, cross-cap number two knots are doubled knot.


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