Marked Positive Handleslide Pentagons in Compression Bodies: Relative Coherence
Let $W:X\to Y_{\mathrm{geom}}$ be a completed oriented compression body with $N\geq 3$ ordered product $1$-handles and a supplied protected three-handle sector. We realize one positive handleslide pentagon by five diffeomorphisms with compatible complete endpoint markings. An isotopy fixed on the entire protected boundary collar identifies the two-edge and three-edge route composites, so the comparison takes place at the level of marked maps rather than homology matrices. The construction fixes the marked disk systems at all five vertices before choosing any edge map, so incident edges use…
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