CASSON-GORDON INVARIANTS OF GENUS ONE KNOTS AND CONCORDANCE TO REVERSES

1996 ◽  
Vol 05 (05) ◽  
pp. 661-677 ◽  
Author(s):  
SWATEE NAIK
Keyword(s):  
Pretzel Knots ◽  
Genus One

For genus one knots the Casson-Gordon invariant τ is expressed in terms of the classical signatures, generalizing an earlier result of P. Gilmer. As an application it is shown that the pretzel knots K(3, –5, 7) and K(3, –5, 17) are not concordant to their reverses.

GENUS ONE, THREE-BRIDGE KNOTS ARE PRETZEL

1999 ◽  
Vol 08 (07) ◽  
pp. 879-885
Author(s):  
SATOSHI FUKUHAMA ◽  
MAKOTO OZAWA ◽  
MASAKAZU TERAGAITO
Keyword(s):  
Pretzel Knots ◽  
Genus One

We prove that genus one, three-bridge knots are pretzel knots.

scholarly journals Sequence of a Coxiella endosymbiont of the tick Amblyomma nuttalli suggests a pattern of convergent genome reduction in the Coxiella genus

2020 ◽  
Author(s):  
Tiago Nardi ◽  
Emanuela Olivieri ◽  
Edward Kariuki ◽  
Davide Sassera ◽  
Michele Castelli
Keyword(s):  
Coxiella Burnetii ◽  
Phylogenetic Analyses ◽  
Genome Reduction ◽  
Metabolic Profiles ◽  
The Novel ◽  
Bacterial Symbionts ◽  
Human Pathogen ◽  
Host Genus ◽  
Supportive Role ◽  
Genus One

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.

scholarly journals Mazur’s rational torsion result for pointless genus one curves: examples

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Arjan Dwarshuis ◽  
Majken Roelfszema ◽  
Jaap Top
Keyword(s):  
Algebraic Geometry ◽  
Elliptic Curves ◽  
Rational Point ◽  
Torsion Points ◽  
Arbitrary Genus ◽  
Mazur’S Theorem ◽  
Genus One

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.

scholarly journals Two-loop superstring five-point amplitudes. Part II. Low energy expansion and S-duality

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Eric D’Hoker ◽  
Carlos R. Mafra ◽  
Boris Pioline ◽  
Oliver Schlotterer
Keyword(s):  
Moduli Space ◽  
Effective Interaction ◽  
Type Ii ◽  
Leading Order ◽  
Effective Interactions ◽  
Heterotic String Theory ◽  
Genus Two ◽  
Genus One ◽  
Graph Function ◽  
Point Amplitude

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.

scholarly journals There are genus one curves of every index over every infinite, finitely generated field

2019 ◽  
Vol 2019 (749) ◽  
pp. 65-86
Author(s):  
Pete L. Clark ◽  
Allan Lacy
Keyword(s):  
Elliptic Curve ◽  
Abelian Variety ◽  
Finitely Generated ◽  
Weil Theorem ◽  
Genus One

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 .

DELTA-UNKNOTTING NUMBER FOR KNOTS

1998 ◽  
Vol 07 (05) ◽  
pp. 639-650 ◽  
Author(s):  
K. NAKAMURA ◽  
Y. NAKANISHI ◽  
Y. UCHIDA
Keyword(s):  
Torus Knots ◽  
Pretzel Knots ◽  
Minimum Number

The Δ-unknotting number for a knot is defined to be the minimum number of Δ-unknotting operations which deform the knot into the trivial knot. We determine the Δ-unknotting numbers for torus knots, positive pretzel knots, and positive closed 3-braids.

CREATING KLEIN BOTTLES BY SURGERY ON KNOTS

2001 ◽  
Vol 10 (05) ◽  
pp. 781-794 ◽  
Author(s):  
MASAKAZU TERAGAITO
Keyword(s):  
Upper Bound ◽  
Klein Bottle ◽  
Dehn Surgery ◽  
The Creation ◽  
Genus One

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.

scholarly journals VIRASORO CORRELATION FUNCTIONS FOR VERTEX OPERATOR ALGEBRAS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250106 ◽  
Author(s):  
DONNY HURLEY ◽  
MICHAEL P. TUITE
Keyword(s):  
Graph Theory ◽  
Vertex Operator ◽  
Generating Functions ◽  
Operator Algebra ◽  
Correlation Functions ◽  
Vertex Operator Algebra ◽  
Operator Algebras ◽  
Vertex Operator Algebras ◽  
Genus Zero ◽  
Genus One

We consider all genus zero and genus one correlation functions for the Virasoro vacuum descendants of a vertex operator algebra. These are described in terms of explicit generating functions that can be combinatorially expressed in terms of graph theory related to derangements in the genus zero case and to partial permutations in the genus one case.

scholarly journals Mealybug (Hemiptera: Pseudococcidae) Species Associated with Cacao Mild Mosaic Virus and Evidence of Virus Acquisition

Insects ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 994
Author(s):  
Alina S. Puig ◽  
Sarah Wurzel ◽  
Stephanie Suarez ◽  
Jean-Philippe Marelli ◽  
Jerome Niogret
Keyword(s):  
Mosaic Virus ◽  
Management Strategies ◽  
Mild Mosaic ◽  
Effective Management ◽  
Coat Protein Region ◽  
Maconellicoccus Hirsutus ◽  
Virus Acquisition ◽  
Mild Mosaic Virus ◽  
Pseudococcus Comstocki ◽  
Genus One

Theobroma cacao is affected by viruses on every continent where the crop is cultivated, with the most well-known ones belonging to the Badnavirus genus. One of these, cacao mild mosaic virus (CaMMV), is present in the Americas, and is transmitted by several species of Pseudococcidae (mealybugs). To determine which species are associated with virus-affected cacao plants in North America, and to assess their potential as vectors, mealybugs (n = 166) were collected from infected trees in Florida, and identified using COI, ITS2, and 28S markers. The species present were Pseudococcus jackbeardsleyi (38%; n = 63), Maconellicoccus hirsutus (34.3%; n = 57), Pseudococcus comstocki (15.7%; n = 26), and Ferrisia virgata (12%; n = 20). Virus acquisition was assessed by testing mealybug DNA (0.8 ng) using a nested PCR that amplified a 500 bp fragment of the movement protein–coat protein region of CaMMV. Virus sequences were obtained from 34.6 to 43.1% of the insects tested; however, acquisition did not differ among species, X2 (3, N = 166) = 0.56, p < 0.91. This study identified two new mealybug species, P. jackbeardsleyi and M. hirsutus, as potential vectors of CaMMV. This information is essential for understanding the infection cycle of CaMMV and developing effective management strategies.

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