Triangulations of non-proper semialgebraic Thom maps
Masahiro Shiota
TL;DR
This paper extends the triangulation results of Thom maps to non-proper semialgebraic and o-minimal definable cases, broadening the scope of triangulability beyond proper maps.
Contribution
It removes the properness condition from Thom's conjecture, proving triangulability for non-proper semialgebraic and o-minimal definable Thom maps.
Findings
Triangulation of non-proper semialgebraic Thom maps established.
Extension of triangulation results to o-minimal structures.
Broader applicability of Thom map triangulation demonstrated.
Abstract
In [5] I solved the Thom's conjecture that a proper Thom map is triangulable. In this paper I drop the properness condition in the semialgebraic case and, moreover, in the definable case in an o-minimal structure.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra