Showing papers on "Equivariant map published in 1985"

Exact Sequences for the Kasparov Groups of Graded Algebras

Abstract: In [11] G. G. Kasparov defined the “operator K-functor” KK(A, B) associated with the graded C*-algebras A and B. If the algebras A and B are trivially graded and A is nuclear he proves six term exact sequence theorems. He asks whether this extends to the graded case. Here we prove such “six-term exact sequence” results in the graded case. Our proof does not use nuclearity of the algebra A. This condition is replaced by a completely positive lifting condition (Theorem 1.1). Using our result we may extend the results by M. Pimsner and D. Voiculescu on the K groups of crossed products by free groups to KK groups [15]. We give however a different way of computing these groups using the equivariant KK-theory developed by G. G. Kasparov in [12]. This method also allows us to compute the KK groups of crossed products by PSL 2(Z).

An Equivariant Sphere Theorem

Abstract: Let M be a connected 3-manifold acted on by a group G. Suppose M has a triangulation invariant under G. In this paper it is shown that if there exists an embedded 2-sphere S which does not bound a 3-ball, then there exists such an S for which gS = S or gS 0 S = 0 for every g e G. This result was proved by Meeks, Simon and Yau [3] using analytic techniques. The proof given here is self-contained and elementary. The proof involves looking at embedded 2-spheres which are in general position with respect to the given triangulation. Such a sphere is called minimal if it does not bound a 3-ball and the number of intersections with the 1-skeleton of the triangulation is the smallest possible. The key result proved in this paper is that given a finite set of minimal spheres satisfying a general position condition, there is a finite set of 'standard' disjoint minimal spheres whose union has the same intersection with the 1-skeleton as the original spheres. The set of disjoint spheres is unique up to a homeomorphism of M which fixes the 2-skeleton. In §4 it is shown that if G\\K is finite then there is a G-equivariant decomposition of M with irreducible factors. We are then able to deduce from the ordinary loop theorem an equivariant version of the projective plane theorem. In §5 the arguments of the previous sections are modified to provide a proof of the equivariant loop theorem [2]. I think that many of the topological results obtained using analytic minimal surface theory can also be derived using the techniques of this paper. I am grateful to Andrew Bartholomew for pointing out an error in an earlier version of this paper. I thank both Peter Scott and the referee for their helpful comments.

Equivariant form of the Deuring-Šafarevič formula for Hasse-Witt invariants

Abstract: Let zc: X ~ Y be a finite Galois covering of connected complete non-singular algebraic curves over an algebraically closed field k. We assume that char k = p > 0 and G = G a l ( X / Y ) is a p-group. This assumption plays an essential role throughout the paper. Put S O = {Q~Ylrc ramifies over Q} and let pel, \" \" , per be the ramification indices with respect to ~z of the points in So(r= ISol and each e i>l) . We denote by 7x and 7y the Hasse-Witt invariants (i.e. p-ranks of the Jacobians) of X and Y,, respectively. Then the Deuring-Safarevi~ formula, which gives a relation between 7x and 7y, is the following equation (see Madan [6], Subrao [121; Deuring [2]; gafarevi~ [91):

A Note on the Covariant Anomaly as an Equivariant Momentum Mapping

Abstract: We show that there is a natural gauge invariant presymplectic structureω on the spaceA of all vector potentials. The covariant axial anomaly\(\tilde G\) is found to be the essentially unique infinitestimally equivariant momentum mapping for the action of the group of gauge transformations on (A,ω). The infinitesimal equivariance of\(\tilde G\) is shown to be equivalent to the Wess-Zumino consistency condition for the consistent axial anomalyG. We also show that theX operator of Bardeen and Zumino, which relatesG and\(\tilde G\), corresponds to the one-form (onA) of the presymplectic structureω.

On spherical space forms with meta-cyclic fundamental group which are isospectral but not equivariant cobordant

Abstract: Ikeda constructed examples of irreducible spherical space forms with meta-cyclic fundamental groups which were isospectral but not isometric. We use the eta invariant of Atiyah-Patodi-Singer to show these examples are not equivariantly cobordant. We show two such examples which are strongly ’171 isospectral are in fact isometric. Compositio Mathematica 56 (1985) -200. © 1985 Martinus Nijhoff Publishers, Dordrecht. Printed in The Netherlands.

Order theoretic classification of monotone equivariant cluster methods

Abstract: In a series of papers, [3], [4] and [5] M. Janowitz has presented an order theoretic model for cluster analysis having its roots in N. Jardine's and R. Sibson's work in numerical taxonomy, [6]. In the Janowitz model, cluster methods are equivalent to mappings from one collection of residuated mappings to another, and two types of cluster methods were characterized in terms of a property called compatibility. We now display a Galois connection behind these characterizations, find all Galois closed objects (thereby establishing all closed sets of Monotone Equivariant cluster methods), and characterize each such object in two distinct ways: one algebraic and one \"practical.\" Note 1.1. The reader might find it helpful to read section 6 of this paper before proceeding to sections 2 through 5. Section 6 discusses the interpretation of the results obtained herein; it may provide motivation and a \"practical\" framework for the more abstract t reatment of the material in sections 2 through 5. It may also illustrate the origins of many of the terms defined throughout this paper.

Aspects of topology: In Memory of Hugh Dowker 1912–1982

Abstract: 1. Obituary: Clifford Hugh Dowker Dona Strauss 2. Knot tabulations and related topics Morwen B. Thistlethwaite 3. How general is a generalized space? Peter T. Johnstone 3. A survey of metrization theory J. Nagata 4. Some thoughts on lattice valued functions and relations M. W. Warner 5. General topology over a base I. M. James 6. K-Dowker spaces M. E. Rudin 7. Graduation and dimension in locales J. Isbell 8. A geometrical approach to degree theory and the Leray-Schauder index J. Dugundji 9. On dimension theory B. A. Pasynkov 10. An equivariant theory of retracts Sergey Antonian 11. P-embedding, LCn spaces and the homotopy extension property Kiiti Morita 12. Special group automorphisms and special self-homotopy equivalences Peter Hilton 13. Rational homotopy and torus actions Stephen Halperin 14. Remarks on stars and independent sets P. Erdos and J. Pach 15. Compact and compact Hausdorff A. H. Stone 16. T1 - and T2 axioms for frames C. H. Dowker and D. Strauss.

Group Actions on Manifolds

Abstract: The work and influence of Deane Montgomery by F. Raymond and R. Schultz Bibliography of Deane Montgomery Homotopy-Theoretic Techniques and Applications: Homotopy invariants and $G$-manifolds: A look at the past fifteen years by R. Schultz Splitting semifree group actions on homotopy spheres into solid tori by R. Dotzel Equivariant Whitehead torsion and actions of compact Lie groups by S. Illman Homological Methods and Machinery: A family of unusual torus group actions by C. Allday For $G=S^1$ there is no $G$-Chern character by J.-P. Haeberly Equivariant frameability of homotopy linear $S^1$ actions on spheres by P. Loffler and R. Schultz Action maps on equivariant function spaces and applications to $PL$ bordism by B. M. Mann and E. Y. Miller Borsuk-Ulam theorems for prime periodic transformation groups by A. Necochea On equivariant maps of Stiefel manifolds by D. Randall Applications of Surgery and Geometric Topology: Representations at fixed points by S. Cappell and J. Shaneson Transformation groups and fixed point data by K. H. Dovermann, T. Petrie, and R. Schultz Lectures on transformation groups and Smith equivalence by M. Masuda and T. Petrie Transformation groups and exotic spheres by R. Schultz Constructions of group actions:A survey of recent developments by S. Weinberger Concordance of group actions on spheres by A. Assadi Induction in equivariant $K$-theory and $s$-Smith equivalence of representations by E. C. Cho and D. Y. Suh Smith equivalent representations of generalized quaternion groups by E. C. Cho $s$-Smith equivalent representations for finite abelian groups by D. Y. Suh Isotropy representations of nonabelian finite group actions by Y. D. Tsai Low-dimensional Topology and Transformation Groups: Transformation groups and low-dimensional manifolds by A. Edmonds Homogeneous Spaces and Seifert Fiberings: The role of Seifert fiber spaces in transformation groups by K. B. Lee and F. Raymond Realizing group automorphisms by D. Fried and R. Lee Cohomology of a Siegel modular variety of degree two by R. Lee and S. Weintraub Transformation Groups and Differential Geometry: Newman's theorem and the Hilbert-Smith conjecture by H. T. Ku, M. C. Ku, and L. N. Mann Geometry, representation theory, and the Yang-Mills functional by H. T. Laquer Problems: Problems submitted to the AMS Summer Research Conference on Group Actions by R. Schultz.

Topology, theory and applications II

Abstract: Vietoris Begle mapping, theorem and transformation groups (N. Alamo, F. Gomez). On coshapes of topological spaces (V.H. Baladze). On a theorem of Runge (M. Bognar). Projective uniform spaces (A.A. Borubaev). On representations of the group of Treofil Knot (M.E. Bozhuyuk). Weakly universal limits of approximate mappings (Z. Cerin). On continuous selections for the hyperspace of subcontinua (J.J. Charatonik). On the topology of resultant hypersurface (A.D.R. Choudary). Simultaneous extensions of screens (A. Csazar). A survey of compatible extensions (77 unsolved problems) (J. Deak). A common topological supercategory for merotopies and syntopogeneous structures (J. Deak). A geometry of homotopically trivial links (D. Dimovski). The connection between the Reidemeister torsion, n-invariant, Rochlin invariant and theta multipliers via the dynamical zeta function (A.L. Fel'shtyn). When do discrete groups act discontinuously? (J. Flachsmeyer). Sequential groups, k-groups and other categories of continuous algebras (R. Fric et al). Discrete Cauchy spaces (S. Gaehler, W. Gaehler). Containing spaces and X-uniformities (D.N. Georgiou, S.D. Iliadis). An equivariant dual J.H.C. Whitehead Theorem (M. Golasinski). Topological aspects of Galois theory for function rings (V.L. Hansen). Four key questions in the theory of 2-to-1 maps (J. Heath). Forgetting and recalling in topology (The concept of excess structure in historical and heuristic perspective) (A.G. Hitchcock). Rim-scattered spaces and the property of universality (S.D. Iliadis, S.S. Zafiridou). The ideal generated by codense sets and the Banach Localization Property (D. Jankovic, T.R. Hamlett). A note on 0-refinable spaces (S. Jiang). On the minimum character of points in compact spaces (I. Juhasz). On M-sequential spaces (L. Kocinac). A theorem on potentially fixed points (W. Kulpa). Nearformities and related topics (D. Leseberg). Fundamental groups of section spaces (J.M. Moller). Countably metacompact, locally countable spaces in the constructible universe (P. Nyikos). On generalized connectivity in bitopological spaces (M.D. Rabrenovic). A polynomial invariant of indexed links (W. Rosicki). On the uniqueness of decomposition of polyhedra into Cartesian product (W. Rosicki). Linear algebra and bifurcation theory, II (S. Rybicki). Triple links in codimension 2 (B.J. Sanderson). Coverings of continua with finitely many ramification points (P. Spyrou). Cauchy nets and completeness in relator spaces (A. Szaz). Universal singular map (A. Szucs). Geometrical proof of a theorem on suspensions in homotopy groups of spheres (A. Szucs). Spaces containing two points not separated by a continuous real-valued function (V. Tzannes). On the homotopy of the gauge transformation groups over three and four dimensional manifolds (V. Zoller).