Nonabelian algebraic topology
R Brown - arXiv preprint math/0407275, 2004 - arxiv.org
This talk gave a sketch of the contents and background to a book with the titleNonabelian
algebraic topology'being written under support of a Leverhulme Emeritus Fellowship (2002 …
algebraic topology'being written under support of a Leverhulme Emeritus Fellowship (2002 …
Unipotent homotopy theory of schemes
S Mondal, E Reinecke - arXiv preprint arXiv:2302.10703, 2023 - arxiv.org
Building on To\" en's work on affine stacks, we develop a certain homotopy theory for
schemes, which we call" unipotent homotopy theory." Over a field of characteristic $ p> 0 …
schemes, which we call" unipotent homotopy theory." Over a field of characteristic $ p> 0 …
Homotopy groups of suspended classifying spaces: an experimental approach
A Romero, J Rubio - Mathematics of computation, 2013 - ams.org
When the results of a computer program are compared to some theorems proved on a
theoretical basis three situations can occur: there can be an agreement between both …
theoretical basis three situations can occur: there can be an agreement between both …
Defining and computing persistent Z-homology in the general case
By general case we mean methods able to process simplicial sets and chain complexes not
of finite type. A filtration of the object to be studied is the heart of both subjects persistent …
of finite type. A filtration of the object to be studied is the heart of both subjects persistent …
Non-Abelian homology and homotopy colimit of classifying spaces for a diagram of groups
AA Husainov - arXiv preprint arXiv:2303.10822, 2023 - arxiv.org
The paper considers non-Abelian homology groups for a diagram of groups introduced as
homotopy groups of a simplicial replacement. It is proved that the non-Abelian homology …
homotopy groups of a simplicial replacement. It is proved that the non-Abelian homology …
Derived functors of nonadditive functors and homotopy theory
L Breen, R Mikhailov - Algebraic & Geometric Topology, 2011 - msp.org
The main purpose of this paper is to extend our knowledge of the derived functors of certain
basic nonadditive functors. The discussion takes place over the integers, and includes a …
basic nonadditive functors. The discussion takes place over the integers, and includes a …
Effective homology of filtered digital images
A Romero, J Rubio, F Sergeraert - Pattern Recognition Letters, 2016 - Elsevier
In this paper, three Computational Topology methods (namely effective homology, persistent
homology and discrete vector fields) are mixed together to produce algorithms for …
homology and discrete vector fields) are mixed together to produce algorithms for …
The second stable homotopy group of the Eilenberg–Maclane space
AE Antony, G Donadze, VP Sivaprasad… - Mathematische …, 2017 - Springer
We prove that for any group G, π _2^ S (K (G, 1)) π 2 S (K (G, 1)), the second stable
homotopy group of the Eilenberg–Maclane space K (G, 1), is completely determined by the …
homotopy group of the Eilenberg–Maclane space K (G, 1), is completely determined by the …
Homotopy cofinality for Non-Abelian homology of group diagrams
AA Husainov - arXiv preprint arXiv:2307.01726, 2023 - arxiv.org
We prove that a homotopy cofinal functor between small categories induces a weak
equivalence between homotopy colimits of pointed simplicial sets. This is used to prove that …
equivalence between homotopy colimits of pointed simplicial sets. This is used to prove that …
Effective persistent homology of digital images
A Romero, J Rubio, F Sergeraert - arXiv preprint arXiv:1412.6154, 2014 - arxiv.org
In this paper, three Computational Topology methods (namely effective homology, persistent
homology and discrete vector fields) are mixed together to produce algorithms for …
homology and discrete vector fields) are mixed together to produce algorithms for …