共查询到20条相似文献,搜索用时 15 毫秒
1.
M. A. Antipov 《Journal of Mathematical Sciences》2007,140(5):611-621
The present paper is one in a series of papers devoted to the classification of some classes of tame algebras up to stable
category equivalence. In this paper, we study symmetric algebras (their stable categories have a structure of triangulated
categories) and the simplest class of tame algebras-the class of special biserial algebras (SB-algebras). In the paper, we give a relevant version of the “diagrammatic method” and study the structure of the triangulated
category “in a neighborhood” of the periodic part (with respect to Ω) of the stable category. Thus we prove the invariance
of the collection of lengths of G-cycles under equivalence of stable categories (see Theorem 2.12). Then we use the invariance
stated above, together with some properties of the Cartan matrix of a symmetric SB-algebra, to prove that the number of A-cycles (but not their lengths!) is also an invariant of stable equivalence. Bibliography:
8 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 330, 2006, pp. 5–28. 相似文献
2.
Ren Guo 《Proceedings of the American Mathematical Society》2007,135(9):3005-3011
In this paper we characterize the edge invariant and Delaunay invariant of a spherical angle structure on a triangulated surface. We also characterize the edge invariant of a hyperbolic angle structure on a triangulated surface.
3.
G. A. Seregin 《Journal of Mathematical Sciences》2007,143(2):2961-2968
We prove some estimates for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations under the
assumption that certain invariant functionals of the velocity field are bounded. Bibliography: 6 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 336, 2006, pp. 199–210. 相似文献
4.
A shaped triangulation is a finite triangulation of an oriented pseudo-three-manifold where each tetrahedron carries dihedral angles of an ideal hyperbolic tetrahedron. To each shaped triangulation, we associate a quantum partition function in the form of an absolutely convergent state integral which is invariant under shaped 3–2 Pachner moves and invariant with respect to shape gauge transformations generated by total dihedral angles around internal edges through the Neumann–Zagier Poisson bracket. Similarly to Turaev–Viro theory, the state variables live on edges of the triangulation but take their values on the whole real axis. The tetrahedral weight functions are composed of three hyperbolic gamma functions in a way that they enjoy a manifest tetrahedral symmetry. We conjecture that for shaped triangulations of closed three-manifolds, our partition function is twice the absolute value squared of the partition function of Techmüller TQFT defined by Andersen and Kashaev. This is similar to the known relationship between the Turaev–Viro and the Witten–Reshetikhin–Turaev invariants of three-manifolds. We also discuss interpretations of our construction in terms of three-dimensional supersymmetric field theories related to triangulated three-dimensional manifolds. 相似文献
5.
A. O. Prishlyak 《Ukrainian Mathematical Journal》1997,49(9):1386-1392
For some knots and links with respect to regular isotopy, we introduce a new invariant, which is a Laurent polynomial in three
variables. The properties of this invariant are studied.
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 9, pp. 1230–1235, September, 1997. 相似文献
6.
I. G. Korepanov 《Theoretical and Mathematical Physics》2009,158(1):82-95
Geometric torsions are torsions of acyclic complexes of vector spaces consisting of differentials of geometric quantities
assigned to the elements of a manifold triangulation. We use geometric torsions to construct invariants for a three-dimensional
manifold with a triangulated boundary. These invariants can be naturally combined into a vector, and a change of the boundary
triangulation corresponds to a linear transformation of this vector. Moreover, when two manifolds are glued at their common
boundary, these vectors undergo scalar multiplication, i.e., they satisfy Atiyah’s axioms of a topological quantum field theory.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 1, pp. 98–114, January, 2009. 相似文献
7.
I. G. Korepanov 《Theoretical and Mathematical Physics》2009,158(3):344-354
We generalize the construction of invariants of three-dimensional manifolds with a triangulated boundary that we previously
proposed for the case where the boundary consists of not more than one connected component to any number of components. These
invariants are based on the torsion of acyclic complexes of geometric origin. An adequate tool for studying such invariants
turns out to be Berezin’s calculus of anticommuting variables; in particular, they are used to formulate our main theorem,
concerning the composition of invariants under a gluing of manifolds. We show that the theory satisfies a natural modification
of Atiyah’s axioms for anticommuting variables.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 405–418, March, 2009. 相似文献
8.
Yu. N. Bibikov 《Mathematical Notes》1997,61(1):29-37
We consider small perturbations with respect to a small parameter ε≥0 of a smooth vector field in ℝn+m possessing an invariant torusT
m. The flow on the torusT
m is assumed to be quasiperiodic withm basic frequencies satisfying certain conditions of Diophantine type; the matrix Ω of the variational equation with respect
to the invariant torus is assumed to be constant. We investigate the existence problem for invariant tori of different dimensions
for the case in which Ω is a nonsingular matrix that can have purely imaginary eigenvalues.
Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 34–44, January, 1997.
Translated by S. K. Lando 相似文献
9.
We construct infinitely many hyperbolic links with x-distance far from the set of (possibly, splittable) alternating links in the concordance class of every link. A sensitive result is given for the concordance class of every (possibly, split) alternating link. Our proof uses an estimate of the τ-distance by an Alexander invariant and the topological imitation theory, both established earlier by the author. 相似文献
10.
Bertrand Toën 《Topology》2004,43(4):765-791
It is now well known that the K-theory of a Waldhausen category depends on more than just its (triangulated) homotopy category (Invent. Math. 150 (2002) 111). The purpose of this note is to show that the K-theory spectrum of a (good) Waldhausen category is completely determined by its Dwyer-Kan simplicial localization, without any additional structure. As the simplicial localization is a refined version of the homotopy category which also determines the triangulated structure, our result is a possible answer to the general question: “To which extent K-theory is not an invariant of triangulated derived categories? ” 相似文献
11.
I. G. Korepanov 《Journal of Mathematical Sciences》1997,83(1):85-92
The tetrahedron equation arises as a generalization of the famous Yang-Baxter equation to the2+1-dimensional quantum field theory and three-dimensional statistical mechanics. Not much is known about its solutions. In the
present paper, a systematic method of constructing nontrivial solutions to the tetrahedron equation with spin-like variables
on the links is described. The essence of this method is the use of the so-called tetrahedral Zamolodchikov algebras. Bibliography:12 titles.
Published inZapiski Nauchnykh Seminarov POMI, Vol. 209, 1994, pp. 137–149.
Translated by I. G. Korepanov. 相似文献
12.
D. A. Kamaev 《Mathematical Notes》1996,60(1):8-17
We prove that to any invariant subset of the dynamical system generated by a one-dimensional quasilinear parabolic equation
there corresponds an invariant family of stable manifolds of finite codimension.
Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 11–23, July, 1996. 相似文献
13.
A number of different polyhedraldecomposition problems have previously been studied, most notably the problem of triangulating a simple polygon. We are concerned with thepolyhedron triangulation problem: decomposing a three-dimensional polyhedron into a set of nonoverlapping tetrahedra whose vertices must be vertices of the polyhedron. It has previously been shown that some polyhedra cannot be triangulated in this fashion. We show that the problem of deciding whether a given polyhedron can be triangulated is NP-complete, and hence likely to be computationally intractable. The problem remains NP-complete when restricted to the case of star-shaped polyhedra. Various versions of the question of how many Steiner points are needed to triangulate a polyhedron also turn out to be NP-hard.This work was supported by National Science Foundation Grant CCR-8809040. 相似文献
14.
V. V. Kapustin 《Journal of Mathematical Sciences》2000,101(3):3088-3092
A new definition of the characteristic function is introduced for contractions on Hilbert spaces. The relationship with other
definitions is established. A factorization formula corresponding to an invariant subspace is obtained. Bibliography: 3 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 71–78.
Translated by V. V. Kapustin. 相似文献
15.
D. V. Treshchev 《Mathematical Notes》1997,61(6):744-757
Generally, the invariant Lagrangian manifolds (stable and unstable separatrices) asymptotic with respect to a hyperbolic torus
of a Hamiltonian system do not coincide. This phenomenon is called separatrix splitting. In this paper, a symplectic invariant
qualitatively describing separatrix splitting for hyperbolic tori of maximum (smaller by one than the number of degrees of
freedom) dimension is constructed. The construction resembles that of the homoclinic invariant found by lazutkin for two-dimensional
symplectic maps and of Bolotin's invariant for splitting of asymptotic manifolds of a fixed point of a symplectic diffeomorphism.
Translated fromMatematicheskie Zametki, Vol. 61, No. 6, pp. 890–906, June, 1997.
Translated by O. V. Sipacheva 相似文献
16.
Let X be a locally compact space with a continuous proper action of a locally compact group G. Assuming that X satisfies a certain kind of duality in equivariant bivariant Kasparov theory, we can enrich the classical construction of
Lefschetz numbers for self-maps to an equivariant K-homology class. We compute the Lefschetz invariants for self-maps of finite-dimensional
simplicial complexes and smooth manifolds. The resulting invariants are independent of the extra structure used to compute
them. Since smooth manifolds can be triangulated, we get two formulas for the same Lefschetz invariant in this case. The resulting
identity is closely related to the equivariant Lefschetz Fixed Point Theorem of Lück and Rosenberg. 相似文献
17.
In Bataineh (2003) [2] we studied the type one invariants for knots in the solid torus. In this research we study the type one invariants for n-component links in the solid torus by generalizing Aicardi's invariant for knots in the solid torus to n-component links in the solid torus. We show that the generalized Aicardi's invariant is the universal type one invariant, and we show that the generalized Aicardi's invariant restricted to n-component links in the solid torus with zero winding number for each component is equal to an invariant we define using the universal cover of the solid torus. We also define and study a geometric invariant for n-component links in the solid torus. We give a lower bound on this invariant using the type one invariants, which are easy to calculate, which helps in computing this geometric invariant, which is usually hard to calculate. 相似文献
18.
We introduce the notion of invariant confidence interval containing the main mass of values for some class of populations, which is independent of the distribution of the population from the given class. It is shown that an invariant one-tail confidence interval for the class of populations with continuous distributions is generated by some order statistic.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 65, pp. 112–117, 1988. 相似文献
19.
B. M. Gurevich 《Theoretical and Mathematical Physics》1992,90(3):289-312
The Liouville operator for an infinite-particle Hamiltonian dynamics corresponding to interaction potentialU is used to introduce the concept of a locally weakly invariant measure on the phase space and to show that if a Gibbs measure with potential of general form is locally weakly invariant then its Hamiltonian is asymptotically an additive integral of the motion of the particles with the interactionU.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 90, No. 3, pp. 424–459, March, 1992. 相似文献
20.
Tim D. Cochran 《Commentarii Mathematici Helvetici》1985,60(1):291-311
A geometric notion of a “derivative” is defined for 2-component links ofS
n inS
n+2 and used to construct a sequenceβ
i
,i=1,2,... of abelian concordance invariants which vanish for boundary links. Forn>1, these generalize the only heretofore known invariant, the Sato-Levine invariant. Forn=1, these invariants are additive under any band-sum and consequently provide new information about which 1-links are concordant
to boundary links. Examples are given of concordance classes successfully distinguished by theβ
i
but not by their
, Murasugi 2-height, Sato-Levine invariant or Alexander polynomial.
Supported in part by a grant from the National Science Foundation. 相似文献