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Normal surface singularities with an integral homology sphere link related to space monomial curves with a plane semigroup
In this article, we consider an infinite family of normal surface singularities with an integral homology sphere link which is related to the family...
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A Note on Rational Band Moves
We introduce an oriented rational band move, a generalization of an ordinary oriented band move, and show that if a knot K in the three-sphere can be...
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Homology Groups and Ideal Class Groups II: Higher-Order Genus Theory
Let M be a rational homology 3-sphere which is a double covering of...
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A note on rational surgeries on a Hopf link
It is clear that every rational surgery on a Hopf link in 3-sphere is a lens space surgery. In this note we give an explicit computation which lens...
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Homology Growth, Hyperbolization, and Fibering
We introduce a hyperbolic reflection group trick which builds closed aspherical manifolds out of compact ones and preserves hyperbolicity, residual...
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Almost simple linear graphs, homology cobordism and connected Heegaard Floer homology
Continuing our previous work in [23], we effectively compute connected Heegaard Floer homologies of two families of Brieskorn spheres realized as...
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The extended persistent homology transform of manifolds with boundary
A shortcoming of persistent homology is that when two domains have different numbers of components or holes the persistence diagrams of any...
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Knot Floer homology and relative adjunction inequalities
We establish inequalities that constrain the genera of smooth cobordisms between knots in 4-dimensional cobordisms. These “relative adjunction...
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Loop coproduct in Morse and Floer homology
By a well-known theorem of Viterbo, the symplectic homology of the cotangent bundle of a closed manifold is isomorphic to the homology of its loop...
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Harmonic representatives in homology over arbitrary fields
We introduce a notion of harmonic chain for chain complexes over fields of positive characteristic. A list of conditions for when a Hodge...
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Upper bounds for the critical values of homology classes of loops
In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of compact manifolds carrying...
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Stability of the symplectomorphism groups of rational surfaces
We apply Zhang’s almost Kähler Nakai–Moishezon theorem and Li–Zhang’s comparison of J -symplectic cones to establish a stability result for the...
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Filtered simplicial homology, graph dissimilarity and überhomology
We introduce a filtration on the simplicial homology of a finite simplicial complex X using bi-colourings of its vertices. This yields two dual...
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Rational model for the string coproduct of pure manifolds
The string coproduct is a coproduct on the homology with field coefficients of the free loop space of a closed oriented manifold introduced by...
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Self-closeness numbers of rational map** spaces
For a closed connected oriented manifold M of dimension 2 n , it was proved by Møller and Raussen that the components of the map** space from M to
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Connected Sums of Sphere Products and Minimally Non-Golod Complexes
We show that if the moment-angle complex \(\mathcal {Z}_K\)...
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On the additivity of strong homology for locally compact separable metric spaces
We show that it is consistent relative to a weakly compact cardinal that strong homology is additive and compactly supported within the class of...