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A Hilbert reciprocity law on 3-manifolds
Based on our homological idelic class field theory, we formulate an analogue of the Hilbert reciprocity law on a rational homology 3-sphere endowed...
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Seiberg–Witten Floer spectra and contact structures
In this article, the author defines an invariant of rational homology 3-spheres equipped with a contact structure as an element of a cohomotopy set...
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On contact type hypersurfaces in 4-space
We consider constraints on the topology of closed 3-manifolds that can arise as hypersurfaces of contact type in standard symplectic
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Lattice Cohomology
First, we define the lattice cohomology associated with the link of a normal surface singularity, whenever this link is a rational homology sphere....
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A Note on a Local Combinatorial Formula for the Euler Class of a PL Spherical Fiber Bundle
We present a local combinatorial formula for the Euler class of an n-dimensional PL spherical fiber bundle as a rational number eCH associated to a...
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Rational double points on Enriques surfaces
We classify, up to some lattice-theoretic equivalence, all possible configurations of rational double points that can appear on a surface whose...
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Surface Singularities, Seiberg–Witten Invariants of Their Links and Lattice Cohomology
The present note aims to focus on certain topological and analytical invariants of complex normal surface singularities and wishes to analyse their...
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Lattices and Correction Terms
Let L be a nonunimodular definite lattice, L ∗ its dual lattice, and λ the discriminant form on L ∗∕L. Using a theorem of Elkies we show that whether...
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Algorithmic aspects of branched coverings II/V: sphere bisets and decidability of Thurston equivalence
We consider Thurston maps : branched self-coverings of the sphere with ultimately periodic critical points, and prove that the Thurston equivalence...
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Examples of Homologically Wide Actions
An action of a finite group G on a manifold M is homologically wide if the first homology of the manifold contains the regular representation of the...
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Suspension spectra of matrix algebras, the rank filtration, and rational noncommutative CW-spectra
In a companion paper (Arone et al. in Noncommutative CW-spectra as enriched presheaves on matrix algebras, ar**v:2101.09775 , 2021) we introduced the...
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Spin Structure and the Framing Skein Module of Links in 3-Manifolds
In this lecture, we show that the only way of changing the framing of a knot or a link by ambient isotopy in an oriented 3-manifold is when the...
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Presentation of Symplectic Map** Class Group of Rational 4-Manifolds
We study the problem of description of the symplectic map** class groups...
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The string topology coproduct on complex and quaternionic projective space
On the free loop space of compact symmetric spaces Ziller introduced explicit cycles generating the homology of the free loop space. We use these...
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The Minkowski norm and Hessian isometry induced by an isoparametric foliation on the unit sphere
Let M t be an isoparametric foliation on the unit sphere ( S n −1 (1), g st ) with d principal curvatures. Using the spherical coordinates induced by M t , we...
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Fibers of Rational Maps and Elimination Matrices: An Application Oriented Approach
Parameterized algebraic curves and surfaces are widely used in geometric modeling and their manipulation is an important task in the processing of...
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Calculating the Homology of the Image
We introduce the alternating homology of a space with a symmetric group action, and give a new construction of the image computing spectral sequence...