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Smooth functions with isolated critical values and systems of fibers

Primarily human-written textHuman understanding: all partsmath.GN — General Topologymath.GR — Group Theorymath.GT — Geometric Topology

Contributed by Naok Kitazawa ↗

Version 1 / Nov 11, 2026 / CC BY 4.0

Abstract

In the 2020s, Marzantowicz and Michalak have introduced the notion of system of smooth hypersurfaces and discussed Morse functions compatible with them: the hypersurfaces are regular level sets of the functions. This is a kind of fundamental theory on Morse functions and related differential topology and geometric topology. We extend this to a certain case: we discuss systems of regular level sets and critical level sets (regular fibers and singular fibers) of smooth functions with isolated critical values.

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Version history

  1. v1 · 8 pagesSubmitted by Naok KitazawaInitial depositCurrentNov 10, 2026