Timeline for Smallest homotopy equivalent space inside a manifold with boundary
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 6, 2016 at 18:20 | comment | added | Ryan Budney | Sometimes it has some good-ish properties. For 4-manifolds one favoured framework for these types of descriptions are called "shadow decompositions" also "spines" are closely related terminology, and also used for 3-manifolds. For 2-manifolds, often one uses trivalent graphs. | |
| Jan 5, 2016 at 13:54 | review | Close votes | |||
| Jan 6, 2016 at 18:29 | |||||
| Jan 5, 2016 at 13:34 | answer | added | Igor Belegradek | timeline score: 6 | |
| Jan 5, 2016 at 13:20 | comment | added | Igor Belegradek | Mohan Ramachandran;s answer in mathoverflow.net/questions/18454/… shows that any open smooth $n$-manifold deformation retracts to a subcomplex of lower dimension. | |
| Jan 5, 2016 at 13:04 | comment | added | user83633 | Given a Morse function, the manifold is homotopy equivalent to a sub-CW-complex with one $n$-cell for each critical point of index $n$. In some examples (if a perfect Morse function exists) this subcomplex should be considered the smallest subspace homotopy equivalent to the manifold. | |
| Jan 5, 2016 at 13:03 | comment | added | Igor Rivin | The OP could mean a lowest-dimensional complex... | |
| Jan 5, 2016 at 12:55 | comment | added | Sean Tilson | I understand what small means in your example because we have some common geometric intuition for euclidean spaces, but how would you compare two spaces? Do you intend to mean some notion of volume (integral of a volume form)? If so I would consider adding some relevant geometry tag. | |
| Jan 5, 2016 at 12:31 | comment | added | Steve Pap | I'm not sure whether this responds to your question, but if your manifold-with-boundary is the unit n-dimensional ball minus its center, what could a solution to your problem look like? | |
| Jan 5, 2016 at 12:19 | history | asked | Dean Barber | CC BY-SA 3.0 |