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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...
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       font style='font-size:12px;'> 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...
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}]...
Knot Contact Homology and Open Strings     Knot Contact Homology  Open Strings       font style='font-size:12px;'> 2014/12/8
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       font style='font-size:12px;'> 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       font style='font-size:12px;'> 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...
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...
Brown's criterion in Bredon homology     Brown's criterion  Bredon homology  Group Theory       font style='font-size:12px;'> 2012/6/21
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       font style='font-size:12px;'> 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, ...
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 ...
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...
We show that if $A$ and $H$ are Hopf algebras that have equivalent tensor categories of comodules, then one can transport what we call a free Yetter-Drinfeld resolution of the counit of $A$ to the sam...
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       font style='font-size:12px;'> 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...

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