Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Isosystolic Inequalities for T^n, RP^n, and M^3   If a closed smooth n-manifold M admits a finite cover whose Z/2Z-cohomology
has the maximal cup-length, then for any riemannian metric g on M, we show that
the systole Sys(M,g) and the volume Vol(M,g) of the riemannian manifold (M,g)
are related by the following isosystolic inequality: Sys(M,g)^n \leq n!
Vol(M,g). The inequality can be regarded as a generalization of Burago and
Hebda's inequality for closed essential surfaces and as a refinement of Guth's
inequality for closed n-manifolds whose Z/2Z-cohomology has the maximal
cup-length. We also establish the same inequality in the context of possibly
non-compact manifolds under a similar cohomological condition. The inequality
applies to (i) T^n and all other compact euclidean space forms, (ii) RP^n and
many other spherical space forms including the Poincar\'e dodecahedral space,
and (iii) most closed essential 3-manifolds including all closed aspherical
3-manifolds.

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The categories of this paper are: math-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th