Konferenz Detail
Sergei Matveev: Special talk
s04.06.2012-05.06.2012
Organisiert von: A. Beliakova
Abstract: We develop a new version of the famous Diamond Lemma [1] and describe several results on prime decompositions of different geometric objects. All results are obtained by using that version and the standard technics for removing intersections of surfaces.1. The Kneser-Milnor prime decomposition theorem of 3-manifolds into connected sums of prime factors (new proof).
2. The similar theorem of Swarup for decompositions into boundary connected sums (new proof).
3. A prime decomposition theorem for knotted graphs in 3-manifolds containing no non-separating 2-spheres.
4. Counterexamples to prime decomposition theorems for knots in 3-manifolds and for 3-orbifolds.
5. A new theorem on annular splittings of 3-manifolds, which is independent of the JSJ-splitting theorem.
6. An existence and uniqueness theorem for prime decompositions of homologically trivial knots in thick surfaces.
7. Prime decomposition theorem for virtual knots.
Reference:
[1] M. H. A. Newman, On theories with a combinatorial definition of "equivalence", Ann. Math. 43 (1942), 223-243.
| Monday, 04.06.12 | |||
| Zeit | Referent | Vortragstitel | Raum |
| 14:00-16:00 | Sergei Matveev (Chelyabinsk State University) | Roots of low-dimensional objects | Y27H28 |
| Tuesday, 05.06.12 | |||
| Zeit | Referent | Vortragstitel | Raum |
| 10:00-12:00 | Sergei Matveev (Chelyabinsk State University) | Roots of low-dimensional objects | Y27H28 |