Timeline for Cobordisms of bundles?
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18, 2010 at 9:58 | comment | added | Michael | In §2 they talk about cobordism of vector bundles (two m-dimensional vector bundles on two manifolds of dimension n are said to be cobordant if there is a vector bundle on an n+1 dimensional manifold which restricts on the boundary to the disjoint union of the former bundles). They say that the resulting cobordism group is isomorphic to the n-th dimensional cobordism group of the classifying space BO(m) -- compare Thorny's answer. This seemed close enough to your question, but maybe I misunderstood? | |
| Jan 18, 2010 at 4:21 | comment | added | jeremy | Maybe I don't have enough background here, but this paper doesn't seem especially enlightening. Its introduction claims it wants to find the conditions for a $k m$ dimensional vector bundle to be cobordant to a Whitney sum of $k$ copies of an $m$-dimensional bundle. Which is not quite what I'm thinking of? The paper also seems to have only two references, neither of which appear to be very helpful... But what I am interested in is the bundle structure on $W$ where $\partial W = E \cup F$. | |
| Jan 17, 2010 at 14:37 | history | answered | Michael | CC BY-SA 2.5 |