o-minimal homotopy and generalized (co)homology (Q350788)

The paper under review continues the development of parts of the machinery of algebraic topology in the setting of o-minimal expansions of fields. Here the author adapts much of the very general semialgebraic homotopy theory due to Delfs and Knebusch (see for example the books [\textit{H. Delfs} and \textit{M. Knebusch}, Locally semialgebraic spaces. Berlin etc.: Springer-Verlag (1985; Zbl 0582.14006); \textit{M. Knebusch}, Weakly semialgebraic spaces. Berlin etc.: Springer-Verlag (1989; Zbl 0681.14008)]). In the words of the author ``the main results of this paper \dots include the comparison theorem, a definable version of the Whitehead theorem and equivalence of [various] homotopy categories''. The author includes many examples to motivate the various definitions and results, although reading the paper will still be easier for those who are familiar with the work of Delfs and Knebusch mentioned above.