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991.
The category of small covariant functors from simplicial sets to simplicial sets supports the projective model structure [B. Chorny, W.G. Dwyer, Homotopy theory of small diagrams over large categories, preprint, 2005]. In this paper we construct various localizations of the projective model structure and also give a variant for functors from simplicial sets to spectra. We apply these model categories in the study of calculus of functors, namely for a classification of polynomial and homogeneous functors. In the n-homogeneous model structure, the nth derivative is a Quillen functor to the category of spectra with Σn-action. After taking into account only finitary functors—which may be done in two different ways—the above Quillen map becomes a Quillen equivalence. This improves the classification of finitary homogeneous functors by T.G. Goodwillie [T.G. Goodwillie, Calculus. III. Taylor series, Geom. Topol. 7 (2003) 645-711 (electronic)]. 相似文献
992.
In this paper we prove the semialgebraic version of Palais' covering homotopy theorem, and use this to prove Bredon's covering mapping cylinder conjecture positively in the semialgebraic category. Bredon's conjecture was originally stated in the topological category, and a topological version of our semialgebraic proof of the conjecture answers the original topological conjecture for topological G-spaces over “simplicial” mapping cylinders. 相似文献
993.
Anna Valette-Stasica 《Topology and its Applications》2007,154(2):443-448
Using algebraically constructible functions we give a generically effective method to detect asymptotic values of polynomial mappings with finite fibers defined on the real plane. By asymptotic variety we mean the set of points at which the polynomial mapping fails to be proper. 相似文献
994.
Crossed modules have longstanding uses in homotopy theory and the cohomology of groups. The corresponding notion in the setting of categorical groups, that is, categorical crosses modules, allowed the development of a low-dimensional categorical group cohomology. Now, its relevance is also shown here to homotopy types by associating, to any pointed CW-complex (X,∗), a categorical crossed module that algebraically represents the homotopy 3-type of X. 相似文献
995.
We construct cellular homotopy theories for categories of simplicial presheaves on small Grothendieck sites and discuss applications to the motivic homotopy category of Morel and Voevodsky. 相似文献
996.
Markus Szymik 《Topology and its Applications》2007,154(11):2323-2332
Let G be a finite group. For semi-free G-manifolds which are oriented in the sense of Waner [S. Waner, Equivariant RO(G)-graded bordism theories, Topology and its Applications 17 (1984) 1-26], the homotopy classes of G-equivariant maps into a G-sphere are described in terms of their degrees, and the degrees occurring are characterised in terms of congruences. This is first shown to be a stable problem, and then solved using methods of equivariant stable homotopy theory with respect to a semi-free G-universe. 相似文献
997.
Let X be a 1-connected CW-complex of finite type and ε?(X) be the group of homotopy classes of self-equivalences of X which induce the identity on homotopy groups. In this paper, we prove that every finitely generated 2-solvable rational nilpotent group is realizable as ε?(X) where X is the rationalization of a 1-connected CW-complex of finite type. 相似文献
998.
Ryuichi Tanaka 《Topology and its Applications》2007,154(15):2849-2855
We describe a finite complex B as I-trivial if there does not exist a Z2-map from Si−1 to S(α) for any vector bundle α over B and any integer i with i>dimα. We prove that the m-fold suspension of projective plane FP2 is I-trivial if and only if m≠0,2,4 for F=C, m≠0,4 for F=H. In the case where F is the Cayley algebra, the m-fold suspension is shown to be I-trivial for every m>0. 相似文献
999.
We study the inverse scattering problem for the nonlinear Schrödinger equation and for the nonlinear Klein–Gordon equation with the generalized Hartree type nonlinearity. We reconstruct the nonlinearity from knowledge of the scattering operator, which improves the known results. 相似文献
1000.
Formation of the liquid state for clusters with a pair interaction between atoms is examined within the framework of the void model, in which configurational excitation of atoms results from formation of voids. Void parameters are found from computer simulation by molecular dynamics methods for Lennard-Jones clusters and from real thermodynamic parameters of the liquid states of condensed inert gases. Phase transitions are analyzed in terms of two aggregate states. This information allows us to divide the entropy jump during the solid-liquid phase transitions in two parts, so that one corresponds to configuration excitation at zero temperature, and the other is a contribution from thermal vibrations of atoms. The latter part contributes from approximately 40% for Lennard-Jones clusters consisting of 13 and 55 atoms up to 56% for bulk inert gases. These magnitudes explain the validity of melting criteria based on thermal motion of atoms, even though this phase transition results from configurational excitation of ensembles of bound atoms. It is shown that the void concept allows us to analyze various aspects of the liquid state of clusters including the existence of the freezing temperature below which no metastable liquid state exists, and the properties of glassy states which may exist below the freezing point. 相似文献