By Giuseppe Zampieri

Cauchy-Riemann (CR) geometry is the research of manifolds outfitted with a method of CR-type equations. in comparison to the early days while the aim of CR geometry was once to provide instruments for the research of the life and regularity of ideas to the $\bar\partial$-Neumann challenge, it has quickly bought a lifetime of its personal and has grew to become a tremendous subject in differential geometry and the research of non-linear partial differential equations. an entire knowing of contemporary CR geometry calls for wisdom of varied themes similar to real/complex differential and symplectic geometry, foliation idea, the geometric conception of PDE's, and microlocal research. these days, the topic of CR geometry is particularly wealthy in effects, and the volume of fabric required to arrive competence is formidable to graduate scholars who desire to examine it. in spite of the fact that, the current publication doesn't goal at introducing the entire issues of present curiosity in CR geometry. as a substitute, an try out is made to be pleasant to the beginner by means of relocating, in a reasonably secure method, from the weather of the speculation of holomorphic services in different advanced variables to complex themes equivalent to extendability of CR features, analytic discs, their infinitesimal deformations, and their lifts to the cotangent house. the alternative of subject matters offers an excellent stability among a primary publicity to CR geometry and topics representing present study. Even a professional mathematician who desires to give a contribution to the topic of CR research and geometry will locate the alternative of issues beautiful

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Additional info for Complex analysis and CR geometry

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L = For a simplex a of L, denotes the barycenter of cr. (2) The fc-skeleton of L is denoted by identify with and We often (3) As in a), mesh L = sup{diam a : a e L}. For a subset S of M, 5T(5, L) denotes the collection of simplexes of L which meet S and st(5, L) = \ST{S,L)\, The same notations apply to cell complexes. (c) When M is a PL manifold, its triangulation is always assumed to be combi­ natorial. The (manifold) boundary is denoted by dM and int M = M - d M . (d) A space X is k-connected {X G C^) if 'Ki{X) = 0 for each i < k.

Barge, Rotation intervals for attractors, in preparation. 2 . K. Alligood and J. Yorke, Accessible saddles on fractal basin boundaries, Ergod. Th. and Dynam. Sys. 12 (1992), 377-400. 3. K. Alligood and J. Yorke, Rotation intervals for chaotic sets, preprint. 4. D. Aronson, M. Chory, G. Hall, R. McGehee, Bifurcations from an invariant circle for two-parameter families of maps of the plane: a computer assisted study, Commun. Math. Phys. 83 (1982), 303-354. 5. M. Barge and R. Gillette, Rotation and periodicity in plane separating continua, Ergod.

A5616 The paper was written while the second author was visiting the University of Saskatchewan. 37 38 CHIGOGIDZE, KAWAMURA AND TYMGHATYN 3. 1. 2. 3. Group actions on Menger manifolds, connections with the Hilbert-Smith conjecture 4. 1. 2. HausdorfF dimension 5. 1. 2. Pseudo-boundaries and pseudo-interiors of Euclidean spaces and Menger compacta 6. 1 . 2. 3. 4. 5. Topological dynamics 1. I n t r o d u c t io n The main purpose of the present paper is to give a survey of the theory of Menger Manifolds and to outline some possible directions for applications of the ideas, techniques and philosophy of the field to other branches of modern geometric topology.