By Michael Charles Crabb, Visit Amazon's Ioan Mackenzie James Page, search results, Learn about Author Central, Ioan Mackenzie James,

Topology occupies a vital place within the arithmetic of this present day. the most beneficial rules to be brought long ago sixty years is the idea that of fibre package, which supplies a suitable framework for learning differential geometry and masses else. Fibre bundles are examples of the type of buildings studied in fibrewise topology. simply as homotopy concept arises from topology, so fibrewise homotopy the­ ory arises from fibrewise topology. during this monograph we offer an summary of fibrewise homotopy conception because it stands at the present. it truly is was hoping that this can stimulate additional study. The literature at the topic is already relatively large yet essentially there's a good deal extra to be performed. Efforts were made to strengthen basic theories of which traditional homotopy idea, equivariant homotopy idea, fibrewise homotopy concept and so on can be detailed instances. for instance, Baues [7] and, extra lately, Dwyer and Spalinski [53], have awarded such normal theories, derived from an past thought of Quillen, yet none of those appear to offer rather the appropriate framework for our reasons. we now have most well-liked, during this monograph, to improve fibre clever homotopy concept roughly ab initio, assuming just a simple wisdom of standard homotopy conception, not less than within the early sections, yet our target has been to maintain the exposition kind of self-contained.