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1.
Let k be a subring of the field of rational functions in x, v,s which contains . If M is an oriented 3-manifold, let denote the Homflypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Homflypt skein relations:
(1) ; (2) L with a positiv e twist ; (3) where O is the unknot. We give two bases for the relative Homflypt skein module of the solid torus with 2 points in the boundary.
The first basis is related to the basis of given by J. Hoste and M. Kidwell and also V. Turaev; the second basis is related to a Young idempotent basis for based on the work of A. Aiston, H. Morton and C. Blanchet. We prove that if the elements , for n a nonzero integer, and the elements , for any integer m, are invertible ink, then -torsion module . Here the free part is generated by the empty link . In addition, if the elements , for m an integer, are invertible in k, then has no torsion. We also obtain some results for more general k.
Received January 7, 2000; in final form September 20, 2000 / Published online April 12, 2001 相似文献
2.
D. Bullock 《Commentarii Mathematici Helvetici》1997,72(4):521-542
Let M be a compact orientable 3-manifold. The set of characters of SL
2()-representations of forms a closed affine algebraic set. We show that its coordinate ring is isomorphic to a specialization of the Kauffman bracket
skein module, modulo its nilradical. This is accomplished by realizing the module as a combinatorial analog of the ring in
which tools of skein theory are exploited to illuminate relations among characters. We conclude with an application, proving
that a small manifold's specialized module is necessarily finite dimensional.
Received: April 18, 1996 相似文献
3.
Charles Frohman Razvan Gelca 《Transactions of the American Mathematical Society》2000,352(10):4877-4888
We prove that the Kauffman bracket skein algebra of the cylinder over a torus is a canonical subalgebra of the noncommutative torus. The proof is based on Chebyshev polynomials. As an application, we describe the structure of the Kauffman bracket skein module of a solid torus as a module over the algebra of the cylinder over a torus, and recover a result of Hoste and Przytycki about the skein module of a lens space. We establish simple formulas for Jones-Wenzl idempotents in the skein algebra of a cylinder over a torus, and give a straightforward computation of the -th colored Kauffman bracket of a torus knot, evaluated in the plane or in an annulus.
4.
Co-Hopfian Modules of Generalized Inverse Polynomials 总被引:2,自引:0,他引:2
Let R be an associative ring not necessarily possessing an identity and (S, ≤) a strictly totally ordered monoid which is also artinian and satisfies that 0 ≤s for any s∈S. Assume that M is a left R-module having propertiy (F). It is shown that M is a co-Hopfian left R-module if and only if [M
S
, ≤] is a co-Hopfian left [[R
S
, ≤]]-module.
Received October 14, 1998, Accepted October 15, 1999 相似文献
5.
Rafal Komendarczyk 《Geometriae Dedicata》2008,134(1):217-238
Let M be a compact orientable Seifered fibered 3-manifold without a boundary, and α an S
1-invariant contact form on M. In a suitable adapted Riemannian metric to α, we provide a bound for the volume Vol(M) and the curvature, which implies the universal tightness of the contact structure ξ = ker α.
相似文献
6.
Józef H. Przytycki 《manuscripta mathematica》2000,101(2):199-207
We show that for the Kauffman bracket skein module over the field of rational functions in variable A, the module of a connected sum of 3-manifolds is the tensor product of modules of the individual manifolds.
Received: 12 January 1998 / Revised version: 15 September 1999 相似文献
7.
B. Khani Robati 《Rendiconti del Circolo Matematico di Palermo》2000,49(3):601-608
Let ℬ be a Banach space of analytic functions defined on the open unit disk. We characterize the commutant ofM
Z
2 (the operator of multiplication by the square of independent variable defined on ℬ) and show that for an operatorS in the commutantM
Z
2 ifSM
Z
2k+1−M
Z
2k+1
S is compact for some nonnegative integerk, thenS=M
ϕ whereϕ is a multiplier of ℬ. Letn be a positive integer andS be an operator in the commutant ofM
Z
n defined on a functional Hilbert spaces of analytic functions. We show that under certain conditionsS has the formM
ϕ.
Research supported by the Shiraz University Grant 78-SC-1188-657. 相似文献
8.
We introduce the notion of rational links in the solid torus. We show that rational links in the solid torus are fully characterized by rational tangles, and hence by the continued fraction of the rational tangle. Furthermore, we generalize this by giving an infinite family of ambient isotopy invariants of colored diagrams in the Kauffman bracket skein module of an oriented surface. 相似文献
9.
Let M be a hyperbolic manifold of finite volume which fibers over the circle with fiber a once punctured torus, and let S be an arbitrary incompressible surface in M. We determine the characteristic Jaco-Shalen-Johannson-submanifold of M−S and show, in particular, that Guts (M, S) is empty.
Received: 02 April 2004 相似文献
10.
Let H be a Hopf algebra with bijective antipode, α, β ∈ Aut
Hopf
(H) and M a finite dimensional (α, β)-Yetter-Drinfeld module. We prove that End(M) endowed with certain structures becomes an H-Azumaya algebra, and the set of H-Azumaya algebras of this type is a subgroup of BQ(k, H), the Brauer group of H. 相似文献
11.
Multiderivations of Coxeter arrangements 总被引:3,自引:0,他引:3
Hiroaki Terao 《Inventiones Mathematicae》2002,148(3):659-674
Let V be an ℓ-dimensional Euclidean space. Let G⊂O(V) be a finite irreducible orthogonal reflection group. Let ? be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H∈? choose α
H
∈V
* such that H=ker(α
H
). For each nonnegative integer m, define the derivation module D
(m)
(?)={θ∈Der
S
|θ(α
H
)∈Sα
m
H
}. The module is known to be a free S-module of rank ℓ by K. Saito (1975) for m=1 and L. Solomon-H. Terao (1998) for m=2. The main result of this paper is that this is the case for all m. Moreover we explicitly construct a basis for D
(m)
(?). Their degrees are all equal to mh/2 (when m is even) or are equal to ((m−1)h/2)+m
i
(1≤i≤ℓ) (when m is odd). Here m
1≤···≤m
ℓ are the exponents of G and h=m
ℓ+1 is the Coxeter number. The construction heavily uses the primitive derivation D which plays a central role in the theory of flat generators by K. Saito (or equivalently the Frobenius manifold structure
for the orbit space of G). Some new results concerning the primitive derivation D are obtained in the course of proof of the main result.
Oblatum 27-XI-2001 & 4-XII-2001?Published online: 18 February 2002 相似文献
12.
Takashi Shioya 《manuscripta mathematica》1999,99(4):509-516
Let M be a compact n-dimensional Riemannian orbifold of Ricci curvature ≥n−1. We prove that for 1 ≤k≤n, the k
th nonzero eigenvalue of the Laplacian on M is equal to the dimension n if and only if M is isometric to the k-times spherical suspension over the quotient S
n
−
k
}Γ of the unit (n−k)-sphere by a finite group Γ⊂O(n−k+1) acting isometrically on S
n
−
k
⊂ℝ
n
−
k
+.
Received: 21 September 1998 / Revised version: 23 February 1999 相似文献
13.
For a given polyhedron K(?)M,the notation RM(K)denotes a regular neigh- borhood of K in M.The authors study the following problem:find all pairs(m,k) such that if K is a compact k-polyhedron and M a PL m-manifold,then R_M(f(K))≌R_M(g(K))for each two homotopic PL embeddings f,g:K→M.It is proved that R_S~(k 2)(S~k)(?)S~k×D~2 for each k(?)2 and some PL sphere S~k(?)S~(k 2)(even for any PL sphere S~k(?)S~(K 2)having an isolated non-locally flat point with the singularity S~(k-1)(?) S~(k 1)such thatπ_1(S~(k 1)-S~(k-1))(?)Z). 相似文献
14.
We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-Xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in S n+1 satisfying Sf 4 f_3~2 ≤ 1/n S~3 , where S is the squared norm of the second fundamental form of M, and f_k =sum λ_i~k from i and λ_i (1 ≤ i ≤ n) are the principal curvatures of M. We prove that there exists a positive constant δ(n)(≥ n/2) depending only on n such that if n ≤ S ≤ n + δ(n), then S ≡ n, i.e., M is one of the Clifford torus S~k ((k/n)~1/2 ) ×S~... 相似文献
15.
Let M be the closed, simply connected, 4-manifold with nonnegative sectional curvature, called a nonnegatively curved 4-manifold, with an effective and isometric Z
m
-action for a positive integer m ≧ 617. Assume that Z
m
acts trivially on the homology of M. The goal of this short paper is to prove that if the fixed point set of any nontrivial element of Z
m
has at most one two-dimensional component, then M is homeomorphic to S
4, #
i
l
=1S
2 × S
2, l = 1, 2, or #
j
k
= 1 ± CP
2, k = 1, 2, 3, 4, 5. The main strategy of this paper is to give an upper bound of the Euler characteristic χ(M) under the homological assumption of a Z
m
-action as above by using the Lefschetz fixed point formula. 相似文献
16.
Let k(x) be the field of fractions of the polynomial algebra k[x] over the field k. We prove that, for an arbitrary finite dimensional k-algebra Λ, any finitely generated Λ ⊗k k(x)-module M such that its minimal projective presentation admits no non-trivial selfextension is of the form M ≅ Nk(x), for some finitely generated Λ-module N. Some consequences are derived for tilting modules over the rational algebra Λ ⊗k k(x) and for some generic modules for Λ.
Received: 24 November 2003; revised: 11 February 2005 相似文献
17.
Heather M. Russell 《Geometriae Dedicata》2009,142(1):71-89
This paper establishes an isomorphism between the Bar-Natan skein module of the solid torus with a particular boundary curve
system and the homology of the (n, n) Springer variety. The results build on Khovanov’s work with crossingless matchings and the cohomology of the (n, n) Springer variety. We also give a formula for comultiplication in the Bar-Natan skein module for this specific three-manifold
and boundary curve system. 相似文献
18.
R. J. Cook 《Proceedings Mathematical Sciences》1989,99(2):147-153
Letf(x)=θ1
x
1
k
+...+θ
s
x
s
k
be an additive form with real coefficients, and ∥α∥ = min {|α-u|:uεℤ} denote the distance fromα to the nearest integer. We show that ifθ
1,…,θ
s
, are algebraic ands = 4k then there are integersx
1,…,x
s
, satisfying l ≤x
1,≤ N and ∥f(x)∥ ≤ N
E
, withE = − 1 + 2/e.
Whens = λk, 1 ≤λ ≤ 2k, the exponentE may be replaced byλE/4, and if we drop the condition thatθ
1,…,θ
s
, be algebraic then the result holds for almost all values of θεℝ
s
. Whenk ≥ 6 is small a better exponent is obtained using Heath-Brown’s version of Weyl’s estimate. 相似文献
19.
Lu Fangyan 《高校应用数学学报(英文版)》1997,12(4):441-446
ESTIMATEFORDISTANCE┐COEFFICIENTOFMATRICESLUFANGYANAbstract.MotivationofthispaperisanopenproblemexposedbyB.Beauzamy[1].LetMbea... 相似文献
20.
M. Domokos 《manuscripta mathematica》2002,108(1):123-133
Let M be a finite dimensional module over a finite dimensional basic K-algebra Λ, where K is an algebraically closed field. We associate with M a weight θ
M
(i.e. an element of the dual of the Grothendieck group of mod-Λ) in module theoretic terms. Let β be a dimension vector with
θ
M
(β)=0. We generalize a construction of relative invariants of quivers due to Schofield [S] and define a relative invariant
polynomial function d
M
β
on the variety of modules of dimension vector β, such that d
M
β
(N) = 0 for some module N if and only if there is a nonzero morphism from M to N. Assuming char (K) = 0, we conclude from the main result of Schofield-Van den Bergh [SV] that relative invariants of this form span all the
spaces of relative invariants. To get algebra generators of the algebra of semi-invariants it is sufficient to take the d
M
β
with M indecomposable.
Received: 31 July 2001 相似文献