Zobrazeno 1 - 10
of 65
pro vyhledávání: '"Gregory Lupton"'
Publikováno v:
Discrete & Computational Geometry. 67:112-165
Digital topology is part of the ongoing endeavour to understand and analyze digitized images. With a view to supporting this endeavour, many notions from algebraic topology have been introduced into the setting of digital topology. But some of the mo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ae8fff4c32eb1b18c052c7a130738d6a
https://doi.org/10.1007/s00454-021-00336-x
https://doi.org/10.1007/s00454-021-00336-x
Autor:
Samuel B. Smith, Gregory Lupton
Publikováno v:
Journal of Homotopy and Related Structures. 15:351-368
Let X be a simply connected space with finite-dimensional rational homotopy groups. Let $$p_\infty :UE \rightarrow B\mathrm {aut}_1(X)$$ be the universal fibration of simply connected spaces with fibre X. We give a DG Lie algebra model for the evalua
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ae8205939c73f670a13e67e7f00729d3
https://doi.org/10.1007/s40062-020-00258-0
https://doi.org/10.1007/s40062-020-00258-0
Autor:
Samuel B. Smith, Gregory Lupton
Publikováno v:
Revista Matemática Complutense. 33:187-196
We prove that the (reduced) rational sectional category of the universal fibration with fibre X, for X any space that satisfies a well-known conjecture of Halperin, equals one.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::60172441c207d1b9c1eb086cd76aa21a
https://doi.org/10.1007/s13163-019-00308-z
https://doi.org/10.1007/s13163-019-00308-z
With a view towards providing tools for analyzing and understanding digitized images, various notions from algebraic topology have been introduced into the setting of digital topology. In the ordinary topological setting, invariants such as the funda
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d8642e5753ae45dbb3c0b5adb7c4db6e
http://arxiv.org/abs/1906.03170
http://arxiv.org/abs/1906.03170
We define a fundamental group for digital images. Namely, we construct a functor from digital images to groups, which closely resembles the ordinary fundamental group from algebraic topology. Our construction differs in several basic ways from previo
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1f3ad2de931790740e6b8080af33a4b5
This paper explores the relation between the structure of fibre bundles akin to those associated to a closed almost nonnegatively sectionally curved manifold and rational homotopy theory.
Comment: 26 pages; comments are welcome!
Comment: 26 pages; comments are welcome!
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c27c22254ee933454884e7c1a73dc25d
Publikováno v:
Algebr. Geom. Topol. 19, no. 4 (2019), 2023-2059
In this paper we study the topological invariant ${\sf {TC}}(X)$ reflecting the complexity of algorithms for autonomous robot motion. Here, $X$ stands for the configuration space of a system and ${\sf {TC}}(X)$ is, roughly, the minimal number of cont
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e36fece2e79407d76593a8dbba9f6ad2
https://projecteuclid.org/euclid.agt/1566439280
https://projecteuclid.org/euclid.agt/1566439280
Autor:
Gregory Lupton, Samuel B. Smith
Publikováno v:
Proceedings of the American Mathematical Society. 144:3619-3633
Which spaces occur as a classifying space for fibrations with a given fibre? We address this question in the context of rational homotopy theory. We construct an infinite family of finite complexes realized (up to rational homotopy) as classifying sp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b71c909066e727d93a5a309541b7ad80
https://doi.org/10.1090/proc/13022
https://doi.org/10.1090/proc/13022
Publikováno v:
Oberwolfach Reports. 13:703-740
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0963294812eea17975060cb17604aeb5
https://doi.org/10.4171/owr/2016/15
https://doi.org/10.4171/owr/2016/15
In arXiv:1711.10132 a new approximating invariant ${\mathsf{TC}}^{\mathcal{D}}$ for topological complexity was introduced called $\mathcal{D}$-topological complexity. In this paper, we explore more fully the properties of ${\mathsf{TC}}^{\mathcal{D}}
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::55cb005477ba18458807df9b92b3902c
http://arxiv.org/abs/1807.03994
http://arxiv.org/abs/1807.03994