## 33 Citations

Open covers, locally sectionable maps, sets of base points, and van Kampen's theorem

- Mathematics
- 2019

We generalize the van Kampen theorem for unions of non-connected spaces, due to R. Brown and A. R. Salleh, to the context where families of subspaces of the base space $B$ are replaced with a `large'…

Fundamental groupoids and homotopy types of non-compact surfaces

- Mathematics
- 2021

The paper contains an application of van Kampen theorem for groupoids to computation of homotopy types of certain class of non-compact foliated surfaces obtained by at most countably many strips R ×…

VAN KAMPEN’S THEOREM FOR LOCALLY SECTIONABLE MAPS

- Mathematics
- 2021

We generalize the Van Kampen theorem for unions of non-connected spaces, due to R. Brown and A. R. Salleh, to the context where families of subspaces of the base space B are replaced with a ‘large’…

Not just an idle game"(the story of higher dimensional versions of the Poincar{\'e} fundamental group)

- Mathematics
- 2021

... the following questions must burningly interest me as a disciple of science: What goal will be reached by the science to which I am dedicating myself? What is essential and what is based only on…

Moderately Discontinuous Homotopy

- MathematicsInternational Mathematics Research Notices
- 2021

We introduce a metric homotopy theory, which we call moderately discontinuous homotopy, designed to capture Lipschitz properties of metric singular subanalytic germs. It matches with the moderately…

Čech closure spaces: A unified framework for discrete and continuous homotopy

- MathematicsTopology and its Applications
- 2021

Amenable category and complexity.

- Mathematics
- 2020

Amenable category is a variant of the Lusternik-Schnirelman category, based on covers by amenable open subsets. We study the monotonicity problem for degree-one maps and amenable category and the…

Lie groupoids and logarithmic connections.

- Mathematics
- 2020

Using tools from the theory of Lie groupoids, we study the category of logarithmic flat connections on principal $G$-bundles, where $G$ is a complex reductive structure group. Flat connections on the…

The knowledge of knots: an interdisciplinary literature review

- PhysicsSpatial Cogn. Comput.
- 2019

This paper presents a review of the literature related to the investigation of knots from the topological, physical, cognitive and computational standpoints, aiming at bridging the gap between pure mathematical work on knot theory and macroscopic physical knots, with an eye to applications and modeling.

Distributed computation of low-dimensional cup products

- Mathematics
- 2018

We describe a distributed algorithm for computing the cup product ∪ : H(X,Z)×H(X,Z)→ H(X,Z) on the cohomology of a finite regular CW-space. A serial implementation of the algorithm is illustrated in…

## References

SHOWING 1-8 OF 8 REFERENCES

Higher-dimensional group theory

- Low-dimensional topology. Proc. Bangor Symp. 1979, Ed. R. Brown and T. L. Thickstun, London Math. Soc. Lecture Note Series 48, 215-238
- 1982

Groupoids and Van Kampen's Theorem

- Mathematics
- 1967

Introduction The fundamental groupoid TT(X) of a topological space X has been known for a long time but has been regarded, usually, as of little import in comparison with the fundamental group—for…

Union theorems for double groupoids and groupoids: some generalisations and applications

- Mathematics
- 1976

The thesis proves Union Theorems for both double groupoids end groupoids and the fundamental groupoid of a space BU ~ssociated to a cover U of X using Brown-Higgins' definition of the homotopy double groupoid p(x,Y,Z).

Categories and groupoids

- van Nostrand Reinhold Mathematical Studies 32
- 1971