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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A link invariant from higher-dimensional Heegaard Floer homology
高维 Heegaard-Floer同调 链接不变量
2023/11/13
We define a higher-dimensional analogue of symplectic Khovanov homology. Consider the standard Lefschetz fibration of a 2n-dimensional Milnor fiber of the A_{k-1} singularity. We represent a link by a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Higher dimensional Heegaard Floer homology and Hecke algebras
高维 希加德弗洛尔同调 赫克代数
2023/4/18
Higher dimensional Heegaard Floer homology (HDHF) is a higher dimensional analogue of Heegaard Floer homology in dimension three. It's partly used to study contact topology in higher dimensions. In a ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Instanton Floer homology and Heegaard diagrams
瞬子 弗洛尔同调和 希加德图
2023/4/21
Instanton Floer homology was introduced by Floer in 1980s and has become a power invariants for three manifolds and knots since then. It has lead to many milestone results, such as the approval of Pro...
Developmental causation and the problem of homology
developmental causation evo-devo homology trait individuation trait inheritance
2016/6/12
While it is generally agreed that the concept of homology refers to individuated traits that have been inherited from common ancestry, we still lack an adequate account of trait individuation or inher...
Structural homology and expression tendency of the natural immune response of the terminal complement components to inoculations in pigs: a review
pigs terminal complement genes homology genetic variation and haemolytic complement activity
2015/4/17
The transmission of infectious agents from domestic animals to humans is a matter of particular concern at present. Inoculation can enhance the defences of each individual animal but only in the short...
Koszul duality of operads and homology of partition posets
Koszul duality operads homology partition posets
2015/3/25
We consider partitions of a set with r elements ordered by refinement. We consider the simplicial complex Kˉ(r) formed by chains of partitions which starts at the smallest element and ends at the larg...
Equivariant homology and K-theory of affine Grassmannians and Toda lattices
Theory of algebra $K $K commutative ring structure
2014/12/25
For an almost simple complex algebraic group G with affine Grassmannian $\text{Gr}_G=G(\mathbb{C}(({\rm t})))/G(\mathbb{C}[[{\rm t}]])$, we consider the equivariant homology $H^{G(\mathbb{C}[[{\rm t}]...
In this thesis, we give a topological interpretation of knot contact homology, by considering intersections of a particular class of chains of open strings with the knot itself. In doing so, we provid...
Statistical Inference For Persistent Homology
persistent homology topology density estimation
2013/4/28
Persistent homology is a method for probing topological properties of point clouds and functions. The method involves tracking the birth and death of topological features as one varies a tuning parame...
A spectral sequence on lattice homology
Lattice homology Heegaard Floer homology spectral sequence
2012/6/29
Using the link surgery formula for Heegaard Floer homology we find a spectral sequence from the lattice homology of a plumbing tree to the Heegaard Floer homology of the corresponding 3-manifold. This...
Combinatorial resolutions of multigraded modules and multipersistent homology
Combinatorial resolutions multigraded modules multipersistent homology Algebraic Topology
2012/6/30
Let $ R=k[x_1...x_r]$ and $M$ a multigraded $R-$module. In this work we interpret $M$ as a multipersistent homology module and give a multigraded resolution of it. The construction involves cellular r...
We translate Brown's criterion for homological finiteness properties to the setting of Bredon homology.
Symmetric Squaring in Homology and Bordism
algebraic topology homology theory bordism Cech homology
2012/6/19
Looking at the cartesian product X \times X of a topological space X with itself, a natural map to be considered on that object is the involution that interchanges the coordinates, i.e. that maps (x, ...
Equivariant semi-topological K-homology and a theorem of Thomason
Equivariant semi-topological K-homology a theorem of Thomason K-Theory and Homology
2012/6/19
We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group. Moreover, we show that Walker's theorem ...
Homological eigenvalues of mapping classes and torsion homology growth for fibered 3--manifolds
Homological eigenvalues mapping classes torsion homology growth fibered 3--manifolds Group Theory
2012/5/9
Let S be an orientable surface with negative Euler characteristic, let \psi\in\Mod(S) be a mapping class of S, and let T_{\psi} be the mapping torus of \psi. We study the action of lifts of \psi on th...