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of 62
pro vyhledávání: '"Pavesic, Petar"'
We introduce the notion of the \emph{equivariant covering type} of a space $X$ on which a finite group $G$ acts, and study its properties. The equivariant covering type measures the size of $G$-equivariant good covers of $X$ and is thus an extension
Externí odkaz:
http://arxiv.org/abs/2309.13423
In a recent publication (D. Govc, W. Marzantowicz, P. Pavesic, Estimates of covering type and the number of vertices of minimal triangulations, Discr. Comp. Geom. 63 (2019), 31-48) we have introduced a new method, based on the Lusternik-Schnirelmann
Externí odkaz:
http://arxiv.org/abs/2108.09853
In this paper we develop a new approach to the study of uncountable fundamental groups by using Hurewicz fibrations with the unique path-lifting property (lifting spaces for short) as a replacement for covering spaces. In particular, we consider the
Externí odkaz:
http://arxiv.org/abs/2101.11457
Autor:
Pavešić, Petar
We give a short proof that, for nice $X$, the based fundamental groupoid of $X$ with topology induced by the compact open topology on the space of paths, is indeed the universal covering space of $X$.
Comment: Short direct proof of a known (but
Comment: Short direct proof of a known (but
Externí odkaz:
http://arxiv.org/abs/2012.15264
Autor:
Pavešić, Petar
Publikováno v:
Algebr. Geom. Topol. 24 (2024) 1713-1723
We study closed orientable manifolds whose topological complexity is at most 3 and determine their cohomology rings. For some of admissible cohomology rings we are also able to identify corresponding manifolds up to homeomorphism.
Externí odkaz:
http://arxiv.org/abs/2011.13754
Autor:
Pavešić, Petar
Publikováno v:
Proceedings of the Royal Society of Edinburgh: Section A Mathematics 151 (2021) 2013-2029
We use some detailed knowledge of the cohomology ring of real Grassmann manifolds $G_k(\mathbb{R}^n)$ to compute zero-divisor cup-length and estimate topological complexity of motion planning for $k$-linear subspaces in $\mathbb{R}^n$. In addition, w
Externí odkaz:
http://arxiv.org/abs/2011.13750
Autor:
Conner, Gregory R., Pavešić, Petar
In his classical textbook on algebraic topology Edwin Spanier developed the theory of covering spaces within a more general framework of lifting spaces (i.e., Hurewicz fibrations with unique path-lifting property). Among other, Spanier proved that fo
Externí odkaz:
http://arxiv.org/abs/2008.11267
Akademický článek
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We compute a lower bound for the number of simplices that are needed to triangulate the Grassmann manifold $G_k(\mathbb{R}^n)$. In particular, we show that the number of top-dimensional simplices grows exponentially with $n$. More precise estimates a
Externí odkaz:
http://arxiv.org/abs/2001.08292
We study a natural generalization of inverse systems of finite regular covering spaces. A limit of such a system is a fibration whose fibres are profinite topological groups. However, as shown in a previous paper (Conner-Herfort-Pavesic: Some anomalo
Externí odkaz:
http://arxiv.org/abs/1901.02108