共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper we study, the Reidemeister zeta function. We prove rationality and functional equations of the Reidemeister zeta function of an endomorphism of finite group. We also obtain these results for eventually commutative endomorphisms. These results are applied to the theory of Reidemeister and Nielsen numbers of self-maps of topological spaces. Our method is to identify the Reidemeister number of a group endomorphism with the number of fixed points in the unitary dual. As a consequence, we show that the Reidemeister torsion of the mapping torus of the unitary dual is a special value of the Reidemeister zeta function. We also prove certain congruences for Reidemeister numbers which are equivalent to a Euler product formula for the Reidemeister zeta function. The congruences are the same as those found by Dold for Lefschetz numbers. 相似文献
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We study an invariant of a 3-manifold which consists of Reidemeister torsion for linear representations which pass through a finite group. We show a Dehn surgery formula on this invariant and compute that of a Seifert manifold over S2. As a consequence we obtain a necessary condition for a result of Dehn surgery along a knot to be Seifert fibered, which can be applied even in a case where abelian Reidemeister torsion gives no information. 相似文献
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Teruaki Kitano 《Proceedings of the American Mathematical Society》2000,128(10):3075-3079
We compute the -Reidemeister torsion of torus bundles over which monodromies are hyperbolic elements in .
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We introduce a topological-type invariant for a cocompact properly discontinuous action of a discrete group on a Riemannian manifold generalizing classical notions of Reidemeister torsion. It takes values in the weak algebraic K-theory of the von Neumann algebra of . We give basic tools for its computation like sum and product formulas and calculate it in several cases. It encompasses, for instance, the Alexander polynomial and is related to analytic torsion. 相似文献
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Dan Burghelea 《Journal of Functional Analysis》2007,248(1):27-78
In the spirit of Ray and Singer we define a complex-valued analytic torsion using non-selfadjoint Laplacians. We establish an anomaly formula which permits to turn this into a topological invariant. Conjecturally this analytically defined invariant computes the complex-valued Reidemeister torsion, including its phase. We establish this conjecture in some non-trivial situations. 相似文献
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N. N. Tarkhanov 《Functional Analysis and Its Applications》2007,41(4):318-322
Quasicomplexes are usually understood as small (in some sense) perturbations of complexes. Of interest are not only perturbations within the category of complexes but also those going beyond this category. A sequence perturbed in this way is no longer a complex, and so it bears no cohomology. We show how to introduce the Euler characteristic for small perturbations of Fredholm complexes. 相似文献
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We give a formula for the Euler characteristic of the Milnor fibre of any analytic function of two variables. This formula depends on the intersection multiplicities, the Milnor numbers and the powers of the branches of the germ of the curve defined by The goal of the formula is that it use neither the resolution nor the deformations of Moreover, it can be use for giving an algorithm to compute it.
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We propose a new way of rewriting the two dimensional Euler equations and derive an original canonical characteristic relation
based on the characteristic theory of hyperbolic systems. This relation contains the derivatives strictly along the bicharacteristic
directions, and can be viewed as the 2D extension of the characteristic relation in 1D case. 相似文献
12.
Let be the circulant graph with . We study the reduced Euler characteristic of the independence complex for with prime and for with odd prime, proving that in both cases does not vanish. We also give an example of circulant graph whose independence complex has
which equals 0, giving a negative answer to R. Hoshino. 相似文献
13.
Let G be a graph which can be embedded in a surface of nonnegative Euler characteristic.In this paper,it is proved that the total chromatic number of G is △(G)+1 if △(G)9,where △(G)is the maximum degree of G. 相似文献
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Euler数和高阶Euler数的推广 总被引:7,自引:0,他引:7
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended. 相似文献
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Krzysztof Koodziejczyk 《Discrete Mathematics》1998,190(1-3)
The boundary characteristic — introduced by Ding and Reay — is a functional defined for a given planar tiling which associates with a given lattice figure, some integer. It appeared to be a very useful parameter to determine the area of lattice figures in the planar tilings with congruent regular polygons. The purpose of this paper is to extend the notion of the boundary characteristic to lattice polyhedra inR3. Studying some of its properties we show, in particular, that it can be applied to determine the volume of lattice polyhedra. 相似文献
17.
《Discrete Mathematics》1998,190(1-3):137-148
The boundary characteristic — introduced by Ding and Reay — is a functional defined for a given planar tiling which associates with a given lattice figure, some integer. It appeared to be a very useful parameter to determine the area of lattice figures in the planar tilings with congruent regular polygons. The purpose of this paper is to extend the notion of the boundary characteristic to lattice polyhedra in
3. Studying some of its properties we show, in particular, that it can be applied to determine the volume of lattice polyhedra. 相似文献
18.
Antonio Breda d'Azevedo Roman Nedela Jozef Sirá n 《Transactions of the American Mathematical Society》2005,357(10):4175-4190
We give a classification of all regular maps on nonorientable surfaces with a negative odd prime Euler characteristic (equivalently, on nonorientable surfaces of genus where is an odd prime). A consequence of our classification is that there are no regular maps on nonorientable surfaces of genus where is a prime such that (mod ) and .
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《Mathematische Nachrichten》2018,291(2-3):398-419
We establish an expression of the Euler characteristic of a r‐regular planar set in function of some variographic quantities. The usual framework is relaxed to a regularity assumption, generalising existing local formulas for the Euler characteristic. We give also general bounds on the number of connected components of a measurable set of in terms of local quantities. These results are then combined to yield a new expression of the mean Euler characteristic of a random regular set, depending solely on the third order marginals for arbitrarily close arguments. We derive results for level sets of some moving average processes and for the boolean model with non‐connected polyrectangular grains in . Applications to excursions of smooth bivariate random fields are derived in the companion paper 25 , and applied for instance to Gaussian fields, generalising standard results. 相似文献
20.
Wolfgang Kreitmeier 《Journal of Mathematical Analysis and Applications》2008,342(1):571-584
For homogeneous one-dimensional Cantor sets, which are not necessarily self-similar, we show under some restrictions that the Euler exponent equals the quantization dimension of the uniform distribution on these Cantor sets. Moreover for a special sub-class of these sets we present a linkage between the Hausdorff and the Packing measure of these sets and the high-rate asymptotics of the quantization error. 相似文献