搜索结果: 1-15 共查到“拓扑学 homology”相关记录21条 . 查询时间(0.109 秒)
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...
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, ...
HF=HM V: Seiberg-Witten-Floer homology and handle addition
Seiberg-Witten-Floer homology handle addition Geometric Topology
2012/4/17
This is the last of five papers that construct an isomorphism between the Seiberg-Witten Floer homology and the Heegaard Floer homology of a given compact, oriented 3-manifold.
Persistent Homology of Filtered Covers
persistent homology nerve lemma topological data analysis
2012/2/29
We prove an extension to the simplicial Nerve Lemma which establishes isomorphism of persistent homology groups, in the case where the covering spaces are filtered. While persistent homology is now wi...
Abstract: We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence...
Hairy graphs and the unstable homology of Mod(g,s), Out(F_n) and Aut(F_n)
Hairy graphs Algebraic Topology
2011/9/20
Abstract: For every cyclic operad O there is an associated Lie algebra hO of positive degree symplectic derivations. For the associative and Lie operads, Kontsevich used his graph homology theory to p...
The link concordance invariant from Lee homology
link concordance invariant Lee homology Geometric Topology
2011/9/19
Abstract: We use the knot homology of Khovanov and Lee to construct link concordance invariants generalizing the Rasmussen $s$-invariant of knots. The relevant invariant for a link is a filtration on ...
Geometry of the Homology Curve Complex
the Homology Curve Complex Geometry Geometric Topology
2011/9/14
Abstract: Suppose $S$ is a closed, oriented surface of genus $g \geq 2$. This paper investigates the geometry of the "homology multicurve complex", $\mathcal{HC}(S,\alpha)$, of $S$; a complex closely ...
Computing the homology of groups: the geometric way
homology of groups the geometric way Algebraic Topology
2011/9/14
Abstract: In this paper we present several algorithms related with the computation of the homology of groups, from a geometric perspective (that is to say, carrying out the calculations by means of si...
On Khovanov-Seidel quiver algebras and bordered Floer homology
Khovanov-Seidel quiver algebras bordered Floer homology Geometric Topology
2011/9/6
Abstract: We discuss a relationship between Khovanov- and Heegaard Floer-type homology theories for braids. Explicitly, we define a filtration on the bordered Heegaard-Floer homology bimodule associat...
A Turaev surface approach to Khovanov homology
Khovanov homology Turaev surface Geometric Topology
2011/9/5
Abstract: We introduce Khovanov homology for ribbon graphs and show that the Khovanov homology of a certain ribbon graph embedded on the Turaev surface of a link is isomorphic to the Khovanov homology...
A rank inequality for the knot Floer homology of double branched covers
the knot Floer homology double branched covers Geometric Topology
2011/9/1
Abstract: Given a knot $K$ in $S^3$, let $\Sigma(K)$ be the double branched cover of $S^3$ over $K$. We show there is a spectral sequence whose $E^1$ page is $(\hat{HFK}(\Sigma(K), K) \otimes V^{n-1})...
Combinatorial knot Floer homology and cyclic double branched covers
Combinatorial knot Floer homology cyclic double branched covers Geometric Topology
2011/8/26
Abstract: Using a Heegaard diagram for the pullback of a knot $K \subset S^3$ in its cyclic double branched cover $\Sigma_2(K)$, we give a combinatorial proof for the invariance of knot Floer homology...
Khovanov Homology
bracket polynomial Khovanov homology cube category simplicial category tangle cobordism chain complex
2011/8/30
Abstract: This paper is an introduction to Khovanov homology.