15,940 research outputs found
Point-pushing in 3-manifolds
We study the Birman exact sequence for compact 3-manifolds.Comment: 33 pages, 1 figure. v2: Incorrect Lemma 6.21 replaced. Corollary 7.4
(now 7.5) strengthened. Other small changes in exposition. An alternative,
more algebraic, proof of Theorem 7.2 (with less exposition) is given in
arXiv:1404.368
The Kakimizu complex of a connected sum of links
We show that |MS(L_1 # L_2)|=|MS(L_1)|\times|MS(L_2)|\times\mathbb{R} when
and are any non-split and non-fibred links. Here denotes
the Kakimizu complex of a link , which records the taut Seifert surfaces for
. We also show that the analogous result holds if we study incompressible
Seifert surfaces instead of taut ones.Comment: 23 pages, 8 figures. This result has been proved independently by
Bassem Saa
The Birman exact sequence for 3-manifolds
We study the Birman exact sequence for compact --manifolds, obtaining a
complete picture of the relationship between the mapping class group of the
manifold and the mapping class group of the submanifold obtained by deleting an
interior point. This covers both orientable manifolds and non-orientable ones.Comment: 30 pages, no figures. v2: Major re-write following referee
suggestions. To appear in Bull. Lond. Math. Soc.; v1: This paper gives an
alternative, more algebraic, proof of the main result of arXiv:1310.7884
(with less exposition
Embedding the Pentagon
The Pentagon Model is an explicit supersymmetric extension of the Standard
Model, which involves a new strongly-interacting SU(5) gauge theory at
TeV-scale energies. We show that the Pentagon can be embedded into an SU(5) x
SU(5) x SU(5) gauge group at the GUT scale. The doublet-triplet splitting
problem, and proton decay compatible with experimental bounds, can be
successfully addressed in this context. The simplest approach fails to provide
masses for the lighter two generations of quarks and leptons; however, this
problem can be solved by the addition of a pair of antisymmetric tensor fields
and an axion.Comment: 39 page
Sato--Tate, cyclicity, and divisibility statistics on average for elliptic curves of small height
We obtain asymptotic formulae for the number of primes for which the
reduction modulo of the elliptic curve \E_{a,b} : Y^2 = X^3 + aX + b
satisfies certain ``natural'' properties, on average over integers and
with and , where and are small relative to .
Specifically, we investigate behavior with respect to the Sato--Tate
conjecture, cyclicity, and divisibility of the number of points by a fixed
integer
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