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Classification of manifolds - Wikipedia
Volume 14 Issue 1 Jan , pp. Finally, we briefly talk about a similar result for strongly quasi-positive links. In this talk, I would like to give an introduction to the bipolar filtration, and prove that every graded quotient of the bipolar filtration has infinite rank. The proof uses higher order amenable Cheeger-Gromov rho invariants and Heegaard Floer d-invariants of infinitely many cyclic branched covers simultaneously. This is joint work with Jae Choon Cha. This talk draws on a combination of independent work, previous joint work with Jake Rasmussen, and work in progress with Rachel Roberts.
These are more elusive objects than one could expect, and, for instance, their classification in the projective plane is not yet complete. I will discuss a symplectic perspective on the problem and some results obtained with Laura Starkston in progress.
Friday June 15 - Irreducible Embeddings and Equivariant Twisted Fiber Sums, Andrew Havens We discuss methods for constructing interesting surface embeddings in 4-manifolds by studying involutions on 4-manifolds. A further potential application of interest is being able to study anti-symplectic involutions on 4-manifolds, and the corresponding geography problem for symplectic 4-manifolds admitting such involutions.
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- L2-invariants and 3–manifolds, I (Stefan Friedl) | Notes!
- Geometric structures on 3 and 4 manifolds, Dubrovnik !
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The process also reframes the "spun embeddings" of Etnyre and Lekili used to describe embeddings of contact 3-manifolds into contact 5-manifolds. We'll discuss obstructions as well as examples including Weinstein 6-manifolds which contain all Weinstein 4-manifolds as properly embedded Weinstein submanifolds.
Torsions of 3-dimensional Manifolds
This is joint work with Amey Kaloti. This allows us to study complex curves via their intersection with these contact level sets, where we can apply three-dimensional tools. Using this perspective, we give a braid-theoretic characterization of the links in Stein-fillable contact manifolds that bound complex curves in their Stein fillings. These theories have very different origins -- representation theory, gauge theory, symplectic topology -- so it's natural to ask for some kind of unifying theory. I will attempt to describe this theory using Bar-Natan's pictorial formulation of link homology.
This strengthens a result of Baldwin, Hedden, and Lobb and proves new functoriality results for several link homology theories. It may also be useful for studying mutation.
I won't assume much specific knowledge of these link homology theories! We then specialise this procedure to knots in S2xS1 , and obtain a lower bound on their geometric winding number. Golla - Satellite operators on knot concordance, Allison Miller The set of knots modulo smooth or topological concordance can be considered with a variety of extra structures, such as the group structure induced by connected sum and the metric induced by the 4-genus function.
Since the classical satellite construction behaves nicely with respect to concordance if K and K' are concordant then P K and P J are concordant for any pattern P , it is natural to ask about the properties of satellite actions with respect to these extra structures. I will briefly survey known results in this area, and then discuss a recent result which gives a complete characterization of when two patterns induce operators which are a bounded distance from each other in terms of winding number.
The Reidemeister Torsion of 3-Manifolds
Diffeomorphisms of Elliptic 3-Manifolds. The Reidemeister torsion of 3-manifolds. The arithmetic of hyperbolic 3-manifolds. Foliations and the geometry of 3-manifolds. The Reidemeister Torsion of 3-Manifolds. Algorithmic topology and classification of 3-manifolds. Homotopy equivalences of 3-manifolds with boundaries. Topology of 3-manifolds and related topics. Algorithmic Topology and Classification of 3-Manifolds.
The geometric topology of 3-manifolds. Quantum invariants of knots and 3-manifolds.
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