Figure 6 - available via license: Creative Commons Attribution 4.0 International
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A schematic of the singular space T . The pink line segment represents Y and the red segment represents P #P .
Source publication
Here we develop the theory of the diagrammatics of surface cross sections to prove that there are an infinite number of homology 3-spheres smoothly embeddable in a homology 4-sphere but not in a homotopy 4-sphere. Our primary obstruction comes from work of Daemi.
Context in source publication
Context 1
... X 1 and X 2 are integer homology balls, they don't affect the definiteness of the intersection form, so it suffices to show for the proof that gluing one of the two X i to W will result in a manifold with no appropriate SUp2q representation. To do this, let W i be the space obtained by gluing X i to W along Y , and let T be the singular space obtained by gluing both X i to W along Y (see Figure 6). Let G i be the image of the inclusion induced map ι : π 1 pW q Þ Ñ π 1 pW i q. ...
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