Zobrazeno 1 - 10
of 53
pro vyhledávání: '"Komendarczyk, Rafal"'
We consider the problem of homotopy-type reconstruction of compact shapes $X\subset\mathbb{R}^N$ that are $\mathrm{CAT}(\kappa)$ in the intrinsic length metric. The reconstructed spaces are in the form of Vietoris--Rips complexes computed from a comp
Externí odkaz:
http://arxiv.org/abs/2406.04259
Autor:
Brooks, Robyn, Komendarczyk, Rafal
We obtain a localized version of the configuration space integral for the Casson knot invariant, where the standard symmetric Gauss form is replaced with a locally supported form. An interesting technical difference between the arguments presented he
Externí odkaz:
http://arxiv.org/abs/2212.12792
Autor:
Komendarczyk, Rafal
In this thesis the author develops techniques to study contact structures via Riemannian geometry. The main observation is a relation between characteristic surfaces of contact structures and zero sets of solutions to certain subelliptic PDEs. This r
Externí odkaz:
http://hdl.handle.net/1853/11517
The based loop space of a configuration space of points in a Euclidean space can be viewed as a space of pure braids in a Euclidean space of one dimension higher. We continue our study of such spaces in terms of Kontsevich's CDGA of diagrams and Chen
Externí odkaz:
http://arxiv.org/abs/2106.11441
Publikováno v:
Fall Workshop on Computational Geometry, New York, 2017
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.
Externí odkaz:
http://arxiv.org/abs/1912.03134
Akademický článek
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Publikováno v:
International Journal of Computational Geometry & Applications Vol. 32 No. 1 (2022) 1-27
We consider the topological and geometric reconstruction of a geodesic subspace of $\mathbb{R}^N$ both from the \v{C}ech and Vietoris-Rips filtrations on a finite, Hausdorff-close, Euclidean sample. Our reconstruction technique leverages the intrinsi
Externí odkaz:
http://arxiv.org/abs/1810.10144
Publikováno v:
Q. J. Math. 71 (2020), no. 2, 729-779
We use rational formality of configuration spaces and the bar construction to study the cohomology of the space of braids in dimension four or greater. We provide a diagram complex for braids and a quasi-isomorphism to the de Rham cochains on the spa
Externí odkaz:
http://arxiv.org/abs/1805.09242
Autor:
Komendarczyk, Rafal.
Publikováno v:
Available online, Georgia Institute of Technology, 2006.
Thesis (Ph. D.)--Mathematics, Georgia Institute of Technology, 2007.
Belegradek, Igor, Committee Member ; Ghrist, Robert, Committee Chair ; Harrell, Evans, Committee Member ; Etnyre, John, Committee Member ; Symington, Margaret, Committee Co-Cha
Belegradek, Igor, Committee Member ; Ghrist, Robert, Committee Chair ; Harrell, Evans, Committee Member ; Etnyre, John, Committee Member ; Symington, Margaret, Committee Co-Cha
Externí odkaz:
http://etd.gatech.edu/theses/available/etd-05192006-231553/
Akademický článek
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