Pure PGR Seminar - Embeddings and knotting of manifolds, Dr Matt Burfitt (Southampton) Seminar
- Time:
- 14:00 - 15:00
- Date:
- 2 May 2018
- Venue:
- Lecture Theatre 10C, Room 10031, Building 54, Mathematical Sciences, University of Southampton, Highfield Campus, SO17 1BJ
For more information regarding this seminar, please email Motiejus Valiunas at M.Valiunas@southampton.ac.uk .
Event details
The classical questions of topology include: deciding when two spaces are homeomorphic, when one space can be embedded in another and when such embeddings are isotopic. The first question is perhaps the most obvious, however in this talk we consider classical results relating to the second two.
Most mathematicians will have come across the subfield of topology known as Knot-theory. Knot-theory is study of knots and links in three dimensional space or more precisely the study of the ambient isotopy case of embedding of one or more copies of S^1 in R^3. This is in general a very hard problem and has received much detailed study. However it is fairly straight forward to show that all embeddings of the circle in R^4 are ambient isotopic, that is, S^1 unknots in R^4.
During this talk we will persure the more general question: what is the smallest dimension in which an m-dimensional smooth manifold can be unknotted? To approach this question it makes sense to first ask, in which dimensions such a manifold can be embedded?
Speaker information
Matt Burfitt , University of Southampton.