Using secondary Upsilon invariants to rule out stable equivalence of knot complexes Samantha Allen. Symmetric homotopy theory for operads Malte Dehling, Bruno Vallette. A new non-arithmetic lattice in PU 3,1 Martin Deraux. An upper bound on the LS-category in presence of the fundamental group Alexander N. Naturality of the contact invariant in monopole floer homology under strong symplectic cobordisms Mariano Echeverria. Roller boundaries for median spaces and algebras Elia Fioravanti. Contracting isometries of CAT 0 cube complexes and acylindrical hyperbolicity of diagram groups Anthony Genevois.

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Topological properties of spaces admitting a coaxial homeomorphism Ross Geoghegan, Craig R. Guilbault, Michael Mihalik. Mapping class groups of covers with boundary and braid group embeddings Tyrone Ghaswala, Alan McLeay. Twisted differential generalized cohomology theories and their Atiyah-Hirzebruch spectral sequence Daniel Grady, Hisham Sati.

On rational homological stability for block automorphisms of connected sums of products of spheres Matthias Grey.

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Algebraic laminations for free products and arational trees Vincent Guirardel, Camille Horbez. Local cut points and splittings of relatively hyperbolic groups Matthew Haulmark. On equivariant and motivic slices Drew Heard. Quasi-right-veering braids and non-loose links Tetsuya Ito, Keiko Kawamuro. Kazez, Rachel Roberts. Ropelength, crossing number and finite type invariants of links Rafal Komendarczyk, Andreas Michaelides. Trisections, intersection forms and the Torelli group Peter Lambert-Cole.

On Kauffman bracket skein modules of marked 3-manifolds and the Chebyshev-Frobenius homomorphism Thang T. Distance one lens space fillings and band surgery on the trefoil knot Tye Lidman, Allison H.

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Moore, Mariel Vazquez. On the genus defect of positive braid knots Livio Liechti. Four genera of links and Heegaard Floer homology Beibei Liu. On spectral sequences from Khovanov homology. Andrew Lobb, Raphael Zentner.

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Unboundedness of some higher Euler classes Kathryn Mann. Treewidth, crushing and hyperbolic volume Clement Maria, Jessica S. The universality of the Rezk nerve Aaron Mazel-Gee. Splitting formulas for the rational lift of the Kontsevich integral Delphine Moussard. On the local homology of Artin groups of finite and affine type Giovanni Paolini. Exponential functors, R-matrices and twists Ulrich Pennig.

This uses instanton gauge theory, and in particular a non-vanishing result of Kronheimer-Mrowka and some new results that we establish for holonomy perturbations of the ASD equation. Using a result of Boileau, Rubinstein and Wang which builds on the geometrization theorem of 3-manifolds , it follows that the fundamental group of any integer homology 3-sphere different from the 3-sphere admits irreducible representations of its fundamental group in SL 2,C.

Obstructing pseudo-convex embeddings of Brieskorn spheres into complex 2-space A Stein manifold is a complex manifold with particularly nice convexity properties. In real dimensions above 4, existence of a Stein structure is essentially a homotopical question, but for 4-manifolds the situation is more subtle. An important question that has been circulating among contact and symplectic topologist for some time asks: whether every contractible smooth 4-manifold admits a Stein structure?

In this talk we will provide examples that answer this question negatively. Moreover, along the way we will provide new evidence to a closely related conjecture of Gompf, which asserts that a nontrivial Brieskorn homology sphere, with either orientation, cannot be embedded in complex 2-space as the boundary of a Stein submanifold.

This is a joint work with Tom Mark. Arnold announced several fruitful conjectures in symplectic topology concerning the number of fixed point of a Hamiltonian diffeomorphism in both the absolute case concerning periodic Hamiltonian orbits and the relative case concerning Hamiltonian chords on a Lagrangian submanifold. The strongest form of Arnold conjecture for a closed symplectic manifold sometimes called the strong Arnold conjecture says that the number of fixed points of a generic Hamiltonian diffeomorphism of a closed symplectic manifold X is greater or equal than the number of critical points of a Morse function on X.

We will discuss the stable version of Arnold conjecture, which is closely related to the strong Arnold conjecture. This is joint work with Georgios Dimitroglou Rizell. Graph formulas for tautological cycles The tautological ring of the moduli space of curves is a subring of the Chow ring that, on the one hand, contains many of the classes represented by "geometrically defined" cycles i. By this I mean that we can explicitly describe a set of additive generators, which are indexed by suitably decorated graphs.

The study of the tautological ring was initiated by Mumford in the '80s and has been intensely studied by several groups of people.

Just a couple years ago, Pandharipande reiterated that we are making progress in a much needed development of a "calculus on the tautological ring", i. An example of such a "calculus" consists in describing formulas for geometrically described classes e.

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In this talk I will explain in what sense "graph formulas" give a good example of what the adjective "meaningful" meant in the previous sentence, and present a few examples of graph formulas. The original work presented is in collaboration with Nicola Tarasca and Vance Blankers. Kuga-Satake construction and cohomology of hyperkahler manifolds Let M be a simple hyperkahler manifold. Kuga-Satake construction gives an embedding of H 2 M,C into the second cohomology of a torus, compatible with the Hodge structure.

This work is joint with A. Soldatenkov and M.

## Casson invariant - Wikipedia

Contact splittings of symplectic rational homology CP 2. We consider splittings of X by a hypersurface of contact type M, where we require M to be a rational homology 3-sphere. We shall go over a few basic properties of such splittings, and then explain how this consideration provides a unified approach to a number of interesting questions in low-dimensional topology, symplectic geometry, as well as in algebraic geometry.

Kevin Walker found an extension of the Casson invariant to rational homology 3-spheres. It is uniquely characterized by the following properties:. In , C. Taubes Boden and C.