2017/03/30 by Vladimer Baladze, Baladze, Vladimer, R. Tsinaridze +1
Mathematics · #54C55 #54C56 #55P55 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1703.10374
openalex publication_date 2017/03/30 · openalex created_date 2017/04/14 · openalex updated_date 2026/07/28
In the paper we construct and develop a fiber strong shape theory for arbitrary spaces over fixed metrizable space \Bo. Our approach is based on the method of Mardešić-Lisica and instead of resolutions, introduced by Mardešić, their fiber preserving analogues are used. The fiber strong shape theory yields the classification of spaces over \Bo which is coarser than the classification of spaces over \Bo induced by fiber homotopy theory, but is finer than the classification of spaces over \Bo given by usual fiber shape theory.