A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
For any link of two components in an integral homology sphere, we define an instanton Floer homology whose Euler characteristic is the linking number between the components of the link. We relate this Floer homology to the Kronheimer-Mrowka instanton Floer homology of knots. We also show that, for two-component links i…
We construct a spectral sequence from the reduced odd Khovanov homology of a link converging to the framed instanton homology of the double cover branched over the link, with orientation reversed. Framed instanton homology counts certain instantons on the cylinder of a 3-manifold connect-summed with a 3-torus. En route…
We prove an excision theorem for the singular instanton Floer homology that allows the excision surfaces to intersect the singular locus. This is an extension of the non-singular excision theorem by Kronheimer and Mrowka and the genus-zero singular excision theorem by Street. We use the singular excision theorem to def…
The instanton Floer homology of a knot in the three-sphere is a vector space with a canonical mod 2 grading. It carries a distinguished endomorphism of even degree,arising from the 2-dimensional homology class represented by a Seifert surface. The Floer homology decomposes as a direct sum of the generalized eigenspaces…
Khovanov-Floer theories are a class of homological link invariants which admit spectral sequences from Khovanov homology. They include Khovanov homology, Szab{ó}'s geometric link homology, singular instanton homology, and various Floer theories applied to branched double covers. In this short note we show that certain …
We prove that Khovanov homology detects the trefoils. Our proof incorporates an array of ideas in Floer homology and contact geometry. It uses open books; the contact invariants we defined in the instanton Floer setting; a bypass exact triangle in sutured instanton homology, proven here; and Kronheimer and Mrowka's spe…
In a recent paper, Lin, Ruberman and Saveliev proved a splitting formula expressing the Seiberg-Witten invariant λSW(X) of a smooth 4-manifold with rational homology of S1×S3 in terms of the Frøyshov invariant h(X) and a Lefschetz number in reduced monopole Floer homology. In this note we observe tha…
Since its inception, Floer homology has been an important tool in low-dimensional topology. Floer theoretic invariants of 3-manifolds tend to be either gauge theoretic or symplecto-geometric in nature, and there is a general philosophy that each gauge theoretic Floer homology should have a corresponding symplectic Fl…
We define four versions of equivariant instanton Floer homology (I+,I−,I∞ and I) for a class of 3-manifolds and SO(3)-bundles over them including all rational homology spheres. These versions are analogous to the four flavors of monopole and Heegaard Floer homology theories. This construction…
Surgery exact triangles in various 3-manifold Floer homology theories provide an important tool in studying and computing the relevant Floer homology groups. These exact triangles relate the invariants of 3-manifolds, obtained by three different Dehn surgeries on a fixed knot. In this paper, the behavior of SU(N)-ins…
We consider a family of corks, denoted Wn, constructed by Akbulut and Yasui. Each cork gives rise to an exotic structure on a smooth 4-manifold via a twist τ on its boundary Σn=∂Wn. We compute the instanton Floer homology of Σn and show that the map induced on the instanton Floer homology by $τ: Σ…
In this paper, we introduce the annular instanton Floer homology which is defined for links in a thickened annulus. It is an analogue of the annular Khovanov homology. A spectral sequence whose second page is the annular Khovanov homology and which converges to the annular instanton Floer homology is constructed. As an…
We show that there is a well-defined cap-product structure on the Fintushel-Stern spectral sequence. Hence we obtain the induced cap-product structure on the ${\BZ}_8$-graded instanton Floer homology. The cap-product structure provides an essentially new property of the instanton Floer homology, from a topological poin…
Taubes proved that the Casson invariant of an integral homology 3-sphere equals half the Euler characteristic of its instanton Floer homology. We extend this result to all closed oriented 3-manifolds with positive first Betti number by establishing a similar relationship between the Lescop invariant of the manifold and…
Around 1988, Floer introduced two important theories: instanton Floer homology as invariants of 3-manifolds and Lagrangian Floer homology as invariants of pairs of Lagrangians in symplectic manifolds. Soon after that, Atiyah conjectured that the two theories should be related to each other and Lagrangian Floer homology…
For each partial flag manifold of SU(N), we define a Floer homology theory for knots in 3-manifolds, using instantons with codimension-2 singularities.