共查询到20条相似文献,搜索用时 15 毫秒
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Paul D. Mitchener Behnam Norouzizadeh Thomas Schick 《Mathematische Nachrichten》2020,293(8):1515-1533
In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse homotopy groups. The main result is that the coarse homotopy groups of a cone over a compact simplicial complex coincide with the usual homotopy groups of the underlying compact simplicial complex. To prove this we develop geometric triangulation techniques for cones which we expect to be of relevance also in different contexts. 相似文献
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Niko Naumann 《Advances in Mathematics》2007,215(2):569-600
We construct the algebraic stack of formal groups and use it to provide a new perspective onto a recent result of M. Hovey and N. Strickland on comodule categories for Landweber exact algebras. This leads to a geometric understanding of their results as well as to a generalisation. 相似文献
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K. A. Hardie 《Topology and its Applications》1991,40(3):265-274
In this note we prove that the coherent homotopy category
over a fixed space B with morphisms represented by certain homotopy commutative squares (see [8]) is isomorphic to the category obtained by formally inverting those maps in the category TopB of topological spaces over B which are ordinary homotopy equivalences. 相似文献
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We study the relations between product decomposition of singular matrices into products of idempotent matrices and product decomposition of invertible matrices into elementary ones. 相似文献
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Varghese Mathai Melvin Rothenberg 《Proceedings of the American Mathematical Society》1998,126(3):887-897
We prove the homotopy invariance of torsion for covering spaces, whenever the covering transformation group is either residually finite or amenable. In the case when the covering transformation group is residually finite and when the cohomology of the covering space vanishes, the homotopy invariance was established by Lück. We also give some applications of our results.
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A. J. Berrick F. R. Cohen Y. L. Wong J. Wu 《Journal of the American Mathematical Society》2006,19(2):265-326
The main results of this article are certain connections between braid groups and the homotopy groups of the -sphere. The connections are given in terms of Brunnian braids over the disk and over the -sphere. The techniques arise from the natural structure of simplicial and -structures on fundamental groups of configuration spaces.
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A nontrivial product in the stable homotopy groups of spheres 总被引:13,自引:0,他引:13
LIU XiuguiInstitute of Mathematics Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2004,47(6):831-841
Let A be the mod p Steenrod algebra for p an arbitrary odd prime. In 1962, Li-uleviciusdescribed hi and bk in Ext (A|*,*) (Zp, Zp) having bigrading (1,2pi(p-1))and (2,2pk+1 x(p - 1)), respectively. In this paper we prove that for p ≥ 7,n ≥ 4 and 3 ≤ s < p - 1, (Zp,Zp) survives to E∞ in the Adams spectral sequence, where q = 2(p - 1). 相似文献
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M. Ghoreishi A. I. B. MD. Ismail A. K. Alomari 《Mathematical Methods in the Applied Sciences》2011,34(15):1833-1842
This paper presents general framework for solving the nth‐order integro‐differential equation using homotopy analysis method (HAM) and optimal homotopy asymptotic method (OHAM). OHAM is parameter free and can provide better accuracy over the HAM at the same order of approximation. Furthermore, in OHAM the convergence region can be easily adjusted and controlled. Comparison, via two examples, between our solution using HAM and OHAM and the exact solution shows that the HAM and the OHAM are effective and accurate in solving the nth‐order integro‐differential equation. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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Michihiro Sakai 《Proceedings of the American Mathematical Society》2001,129(8):2461-2466
The homotopy push-out and pull-back lemma of Iwase (1998) is a generalized version of Theorem 1.1 of Ganea (1965) and the Theorem of Rutter (1971) whose proofs were given under the simply-connectivity condition. The purpose of this paper is to give a proof in the general case.
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Motivated by numerical examples in solving semilinear elliptic PDEs for multiple solutions, some properties of Newton homotopy continuation method, such as its continuation on symmetries, the Morse index, and certain functional structures, are established. Those results provide useful information on selecting initial points for the method to find desired solutions. As an application, a bifurcation diagram, showing the symmetry/peak breaking phenomena of the Henon equation, is constructed. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008 相似文献
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Robert M. Guralnick 《Proceedings of the American Mathematical Society》2007,135(3):689-693
We show that if is a reductive group, then th roots of conjugacy classes are a finite union of conjugacy classes, and that if is an algebraic overgroup of , then the intersection of with a conjugacy class of is a finite union of -conjugacy classes. These results follow from results on finiteness of unipotent classes in an almost simple algebraic group.
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Ju.T. Lisica 《Topology and its Applications》2010,157(17):2715-2735
Three data are interesting here: domains of integration, integrands and integration itself. There is a lack of symmetry between polyhedral chains as domains of integration and differential forms as integrands. The non-symmetric situation disappears after considering the topological spaces of the de Rham differential forms and forms with compact supports and their strong duals, i.e., currents with compact supports and currents, respectively. This idea goes back to Schwartz distributions and Schwartz distributions with compact supports, in other terminology, generalized functions and generalized functions with compact supports.Some problems are raised, e.g., whether every quasi-complete barreled nuclear space E, whose strongly dual E′ is nuclear, is strongly hereditary reflexive. This concerns the above mentioned de Rham spaces. Problems on R- and Q-homotopy, proper R- and Q-homotopy and proper R- and Q-homotopy at infinity are also considered as well as the coalgebra structure on currents and currents with compact supports.The classical theorem concerning derivation of additive functions with respect to volumes in points is generalized to a theorem on derivation of continuous m-forms with compact supports ωm of an oriented n-dimensional C1-manifold Mn with respect to its m-dimensional oriented submanifolds Vm in compact regular oriented submanifolds Lk of Mn, 0?k<m?n. 相似文献
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Waclaw Marzantowicz Klaudiusz Wó jcik 《Proceedings of the American Mathematical Society》2007,135(8):2637-2647
In this note we show that the existence of a periodic segment for a non-autonomous ODE with periodic coefficients implies the existence of infinitely many periodic solutions inside this segment provided that a sequence of Lefschetz numbers of iterations of an associated map is not constant. In the case when this sequence is bounded we have to impose a geometric condition on the segment to get solutions by use of symbolic dynamics.
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Anand Dessai 《Geometriae Dedicata》2002,90(1):49-62
We give bordism-finiteness results for smooth S
3-manifolds. Consider the class of oriented manifolds which admit an S
1-action with isolated fixed points such that the action extends to an S
3-action with fixed point. We exhibit various subclasses, characterized by an upper bound for the Euler characteristic and properties of the first Pontryagin class p
1, for example p
1 = 0, which contain only finitely many oriented bordism types in any given dimension. Also we show finiteness results for homotopy complex projective spaces and complete intersections with S
3-action as above. 相似文献
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Beno Eckmann 《Expositiones Mathematicae》2004,22(4):385-393
The existence of a social choice model on a preference space P is a topological, even homotopical problem. It has been solved 50 years ago, under different terminology, by the author and, a little later, jointly with T. Ganea and P.J. Hilton. P must be an H-space and either contractible or homotopy equivalent to a product of Eilenberg-MacLane spaces over the rationals. 相似文献
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Yildiray Ozan 《Geometriae Dedicata》2004,108(1):131-140
Let X
0 be a topological component of a nonsingular real algebraic variety and i:X → X
C
is a nonsingular projective complexification of X. In this paper, we will study the homomorphism on homotopy groups induced by the inclusion map i:X
0 → X
C
and obtain several results using rational homotopy theory and other standard tools of homotopy theory. 相似文献