Estimates of covering type and minimal triangulations based on category weight
-
Dejan Govc
Abstract
In a recent publication
[D. Govc, W. A. Marzantowicz and P. Pavešić,
Estimates of covering type and the number of vertices of minimal triangulations,
Discrete Comput. Geom. 63 2020, 1, 31–48],
we have introduced a new method, based on
the Lusternik–Schnirelmann category and the cohomology ring of a space X, that yields lower bounds
for the size of a triangulation of X. In this current paper, we present an important extension
that takes into account the fundamental group of X. In fact, if
Funding source: Javna Agencija za Raziskovalno Dejavnost RS
Award Identifier / Grant number: N1-0083
Award Identifier / Grant number: N1-0083
Award Identifier / Grant number: N1-0064
Funding source: Narodowe Centrum Nauki
Award Identifier / Grant number: UMO-2018/30/Q/ST1/00228
Funding statement: Dejan Govc was supported by the Slovenian Research Agency program P1-0292 and grant number N1-0083. Wacław Marzantowicz was supported by the Polish Research Grant NCN Sheng 1 UMO-2018/30/Q/ST1/00228. Petar Pavešić was supported by the Slovenian Research Agency program P1-0292 and grants numbers N1-0083, N1-0064.
Acknowledgements
The authors wish to express their thanks to Mahender Singh and Ergün Yalçin for helpful conversations on group actions on products of spheres and to John Oprea for his advice on the properties of category weight. We are also grateful to the anonymous referee whose comments led to several changes that considerably improved the readability of this paper.
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Articles in the same Issue
- Frontmatter
- Approximating the group algebra of the lamplighter by infinite matrix products
- Shift invariance and reflexivity of compressions of multiplication operators
- Non-invariant deformations of left-invariant complex structures on compact Lie groups
- On the gaps between consecutive primes
- Trivial cup products in bounded cohomology of the free group via aligned chains
- Iwasawa invariants for elliptic curves over ℤp-extensions and Kida's formula
- Estimates of covering type and minimal triangulations based on category weight
- Coherent categorical structures for Lie bialgebras, Manin triples, classical r-matrices and pre-Lie algebras
- Stable vector bundles on generalized Kummer varieties
- Dirac series for complex 𝐸7
- On order of vanishing of characteristic elements
- On transitivity-like properties for torsion-free Abelian groups
- Reverse convolution inequalities for Lebedev–Skalskaya transforms
- Existence of weak solutions to a general class of diffusive shallow medium type equations
Articles in the same Issue
- Frontmatter
- Approximating the group algebra of the lamplighter by infinite matrix products
- Shift invariance and reflexivity of compressions of multiplication operators
- Non-invariant deformations of left-invariant complex structures on compact Lie groups
- On the gaps between consecutive primes
- Trivial cup products in bounded cohomology of the free group via aligned chains
- Iwasawa invariants for elliptic curves over ℤp-extensions and Kida's formula
- Estimates of covering type and minimal triangulations based on category weight
- Coherent categorical structures for Lie bialgebras, Manin triples, classical r-matrices and pre-Lie algebras
- Stable vector bundles on generalized Kummer varieties
- Dirac series for complex 𝐸7
- On order of vanishing of characteristic elements
- On transitivity-like properties for torsion-free Abelian groups
- Reverse convolution inequalities for Lebedev–Skalskaya transforms
- Existence of weak solutions to a general class of diffusive shallow medium type equations
