The Goldman bracket characterizes homeomorphisms
Siddhartha Gadgil
TL;DR
This paper proves that a homotopy equivalence between certain surfaces is a homeomorphism if and only if it preserves the Goldman bracket, linking algebraic properties to topological equivalences.
Contribution
It establishes a new criterion for surface homeomorphisms based on the Goldman bracket, connecting algebraic and topological structures.
Findings
Homotopy equivalences commuting with the Goldman bracket are homeomorphisms.
The Goldman bracket characterizes surface homeomorphisms.
Provides a new algebraic-topological characterization of surface mappings.
Abstract
We show that a homotopy equivalence between compact, connected, oriented surfaces with non-empty boundary is homotopic to a homeomorphism if and only if it commutes with the Goldman bracket.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Algebraic structures and combinatorial models