General Topology-I

Combinatorial Group Theory: COMBINATORIAL GROUP THEORY

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Infinite Abelian Groups

What do you do to start reading dimension theory? Searching the book that you love to read first or find an interesting book that will make you want to read? Everybody has difference with their reason of reading a book. Actuary, reading habit must be from earlier. Many people may be love to read, but not a book. It's not fault. Someone will be bored to open the thick book with small words to read. In more, this is the real condition. So do happen probably with this dimension theory.

Aspects of topology: On dimension theory

This chapter and the next are adapted from a lecture published in the Proceedings of the Third Physics Workshop, held at the Institute of Theoretical and Experimental Physics, Moscow, in 1975. They focus on the uses of homotopy theory in physics, and especially on the calculation of homotopy groups. The next chapter summarizes briefly the ways in which homotopy theory can be applied to quantum field theory.

Elements of Homotopy Theory

Free σ-products and noncommutatively slender groups

The fundamental groups of one-dimensional spaces

The fundamental groups of one-dimensional spaces and spatial homomorphisms

Griffiths [11] gave a presentation of the fundamental group of ( and the proof was completed by Morgan and Morrison [15]. The same group is presented as the free σ-product nσ. : of integers : in [4, Appendix]. Hence the first integral singular homology group H \" (() is the abelianization of the group nσ. :. These results have been generalized to non-metrizable counterparts ( I of ( (see Section 3). In Section 2 we prove that H \" (X ) is torsion-free and H i (X ) ̄ 0 for each onedimensional normal space X and for each i& 2. The result for i& 2 is a slight generalization of [2, Theorem 5]. In Section 3 we provide an explicit presentation of H \" (() and also H \" (( I ) by using results of [4]. Throughout this paper, a continuum means a compact connected metric space and all maps are assumed to be continuous. All homology groups have the integers : as the coefficients. The bouquet with n circles 5n j=\" C j is denoted by B n . The base point (0, 0) of B n is denoted by o for simplicity.

Katsuya Eda

Papers

Free σ-products and noncommutatively slender groups

The fundamental groups of one-dimensional spaces

The fundamental groups of one-dimensional spaces and spatial homomorphisms

The Singular Homology of the Hawaiian Earring

On a Boolean power of a torsion free Abelian group