What question did this study set out to answer?

This research aims to explore the topology of Milnor boundaries associated with real analytic singularities.

February 21, 2026Mathematische Zeitschrift0 citationsOpen Access

On the topology of the Milnor boundary for real analytic singularities

RSR. Araújo dos Santos AMA. Menegon MRMaico F. Ribeiro

Key Points

This research aims to explore the topology of Milnor boundaries associated with real analytic singularities.
Examine the boundaries of Milnor fibers for different real analytic map-germs
Apply tube fibration concepts to the mappings
Investigate specific cases of projections between dimensional spaces.
Identified key properties of the topology of the Milnor boundaries
Showed how the boundaries behave under projections
Revealed implications for different dimensions of map-germs.

Abstract

Abstract We study the topology of the boundaries F₅ ∂ F f and F₈ ∂ F I of the Milnor fibers F₅ F f and F₈, F I, respectively, of real analytic map-germs f: \, (RM, 0) (RK, 0) f: (R M, 0) → (R K, 0) and f₈: = ₈ f: \, (RM, 0) (RI, 0) f I: = Π I ∘ f: (R M, 0) → (R I, 0) that admit Milnor’s tube fibrations, where ₈: \, ({R}K, 0) ({R}^I, 0) Π I: (R K, 0) → (R I, 0) is the canonical projection for 1 I 1 ≤ I K. For each I we prove that the Milnor boundary F₈ <mml: mi

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