connected sum
Let and be two -manifolds. Choose points and , and let be neighborhoods of these points, respectively. Since and are manifolds, we may assume that and are balls, with boundaries homeomorphic to -spheres, since this is possible in . Then let be a homeomorphism. If and are oriented, this should be orientation preserving with respect to the induced orientation (that is, degree 1). Then the connected sum is and glued along the boundaries by .
That is, is the disjoint union of and modulo the equivalence relation if , and .
Title | connected sum |
---|---|
Canonical name | ConnectedSum1 |
Date of creation | 2013-03-22 13:17:59 |
Last modified on | 2013-03-22 13:17:59 |
Owner | bwebste (988) |
Last modified by | bwebste (988) |
Numerical id | 6 |
Author | bwebste (988) |
Entry type | Definition |
Classification | msc 57-00 |