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**1 - 6**of**6**### INTERACTIONS OF STRINGS AND EQUIVARIANT HOMOLOGY THEORIES

"... Abstract. We introduce the notion of the space of parallel strings with par-tially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to con-struct a machinery which produces equivariant generalized homology the ..."

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Abstract. We introduce the notion of the space of parallel strings with par-tially summable labels, which can be viewed as a geometrically constructed group completion of the space of particles with labels. We utilize this to con-struct a machinery which produces equivariant generalized homology theories from such simple and abundant data as partial monoids. 1.

### Interactions and Collisions from the Homotopy Point of View

"... We call an “interaction” the collision of two particles which results in possibly some transfer of data or simply in the annihilation of the particles. In this expository note, we discuss how these situations occur in algebraic topology, and how they give rise to classifying spaces and/or mapping sp ..."

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We call an “interaction” the collision of two particles which results in possibly some transfer of data or simply in the annihilation of the particles. In this expository note, we discuss how these situations occur in algebraic topology, and how they give rise to classifying spaces and/or mapping spaces. We expand on various classical results and give some applications as well.

### A SIMPLE SOLUTION FOR A GROUP COMPLETION PROBLEM

"... Let X be a space with base point. We denote by ΣX the reduced suspension on X and by ΩX the space of based loops on X. Σ and Ω are self functors on the category of compactly generated spaces and left and right adjoint to each other. Thus the composite of their iterations ΩnΣn constitute a monad and ..."

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Let X be a space with base point. We denote by ΣX the reduced suspension on X and by ΩX the space of based loops on X. Σ and Ω are self functors on the category of compactly generated spaces and left and right adjoint to each other. Thus the composite of their iterations ΩnΣn constitute a monad and plays an