Related papers: Monopole Invariants for Webs and Foams
We define three different types of spanning surfaces for knots in thickened surfaces. We use these to introduce new Seifert matrices, Alexander-type polynomials, genera, and a signature invariant. One of these Alexander polynomials extends…
We survey a (nonlinear) Fredholm theory for a new class of ambient spaces called polyfolds, and develop the analytical foundations for some of the applications of the theory. The basic feature of these new spaces, which can be finite and…
We investigate symmetry properties of peculiar modules, a Heegaard Floer invariant of 4-ended tangles which the author introduced in [arXiv:1712.05050]. In particular, we give an almost complete answer to the geography problem for…
This is the first of five papers that construct an isomorphism between the embedded contact homology and Seiberg-Witten Floer cohomology of a compact 3-manifold with a given contact 1-form. This paper describes what is involved in the…
We study the monopole Floer homology of a SOLV rational homology sphere Y from the point of view of spectral theory. Applying ideas of Fourier analysis on solvable groups, we show that for suitable SOLV metrics on Y, small regular…
Let M be a rational homology sphere plumbed 3-manifold associated with a connected negative definite plumbing graph. We show that its Seiberg-Witten invariants equal certain coefficients of an equivariant multivariable Ehrhart polynomial.…
We incorporate pearly Floer trajectories into the transversality scheme for pseudoholomorphic maps introduced by Cieliebak-Mohnke. By choosing generic domain-dependent almost complex structures we obtain zero and one-dimensional moduli…
We introduce a new invariant for foliations using the even pairing between K-homology and cyclic homology and discuss some possible applications in physics.
New estimates are derived concerning the behavior of self-dual hamonic 2-forms on a compact Riemannian 4-manifold with non-trivial Seiberg-Witten invariants. Applications include a vanishing theorem for certain Seiberg-Witten invariants on…
In arXiv:1911.08213 it was conjectured that the compactly supported cohomology of the $m$-th restricted contact locus of an isolated hypersurface singularity coincides, up to a shift, with the Floer cohomology of the $m$-th iterate of the…
Consider the cotangent bundle of a closed Riemannian manifold and an almost complex structure close to the one induced by the Riemannian metric. For Hamiltonians which grow for instance quadratically in the fibers outside of a compact set,…
We use localization formulas in the theory of equivariant cohomology to rederive the wall crossing formulas of Li-Liu and Okonek-Teleman for Seiberg-Witten invariants.
We prove that the pair-of-pants product on the Floer homology of the cotangent bundle of a compact manifold M corresponds to the Chas-Sullivan loop product on the singular homology of the loop space of M. We also prove related results…
In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology-- for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology…
These are notes from lectures given at the Clay Institute Summer School on "Floer homology, gauge theory and low-dimensional topology" (Budapest, 2004). The first part describes as background some of the geometry of symplectic fibre bundles…
We prove Furuta-type bounds for the intersection forms of spin cobordisms between homology 3-spheres. The bounds are in terms of a new numerical invariant of homology spheres, obtained from Pin(2)-equivariant Seiberg-Witten Floer K-theory.…
This is a survey article on the stable cohomotopy refinement of Seiberg-Witten invariants containing also new results, for example: - Stable cohomotopy groups describe path components of certain mapping spaces. - Relation of stable…
Spectral invariants are quantitative measurements in symplectic topology coming from Floer homology theory. We study their dependence on the choice of coefficients in the context of Hamiltonian Floer homology. We discover phenomena in this…
Following a proposal of Fukaya-Ono and the exploration by B. Parker, we introduce a new transversality condition, the FOP transversality condition, for sections of orbifold vector bundles $\mathcal{E} \rightarrow \mathcal{U}$ when both…
This paper considers the invariance of knot Floer homology in a purely algebraic setting, without reference to Heegaard diagrams, holomorphic disks, or grid diagrams. We show that (a small modification of) Ozsv\'ath and Szab\'o's cube of…