Enumerative properties of triangulations of spherical bundles over S 1
We give a complete characterization of all possible pairs ( f 0 , f 1 ) , where f 0 is the number of vertices and f 1 is the number of edges, of any triangulation of an S k -bundle over S 1 . The main point is that Kühnel’s triangulations of S 2 k + 1 × S 1 and the nonorientable S 2 k -bundle over S...
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| Published in | European journal of combinatorics Vol. 29; no. 3; pp. 662 - 671 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.04.2008
|
| Online Access | Get full text |
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| Summary: | We give a complete characterization of all possible pairs
(
f
0
,
f
1
)
, where
f
0
is the number of vertices and
f
1
is the number of edges, of any triangulation of an
S
k
-bundle over
S
1
. The main point is that Kühnel’s triangulations of
S
2
k
+
1
×
S
1
and the nonorientable
S
2
k
-bundle over
S
1
are unique among all triangulations of
(
n
−
1
)
-dimensional homology manifolds with
2
n
+
1
vertices, first Betti number nonzero, and whose orientation double cover has vanishing second Betti number. |
|---|---|
| ISSN: | 0195-6698 1095-9971 |
| DOI: | 10.1016/j.ejc.2007.03.005 |