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Article overview
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Shadows of 4-manifolds with complexity zero and polyhedral collapsing | Hironobu Naoe
; | Date: |
1 May 2016 | Abstract: | Our purpose is to classify acyclic 4-manifolds having shadow complexity zero.
In this paper, we focus on structures of almost-special polyhedra and discuss
this problem combinatorially. We prove that any polyhedral collapsing does not
change 4-manifolds obtained by Turaev’s reconstruction from almost-special
polyhedra before and after collapsing. We also show that any acyclic simple
polyhedron without true vertices can collapse onto a disk. As a consequence of
these results, we prove that any acyclic 4-manifold having shadow complexity
zero with boundary is diffeomorphic to a 4-ball. | Source: | arXiv, 1605.0250 | Services: | Forum | Review | PDF | Favorites |
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