Freeness of hyperplane arrangement bundles and local homology of arrangement complements

The Tutte polynomial is originally a bivariate polynomial which enumerates the colorings of a graph and of its dual graph. Ardila extended in 2007 the definition of the Tutte polynomial on the real hyperplane arrangements. He particularly computed the Tutte polynomials of the hyperplane arrangements associated to the classical Weyl groups. Those associated to the exceptional Weyl groups were computed by De Concini and Procesi one year later. This paper has two objectives: On the one side, we extend the Tutte polynomial computing to the complex hyperplane arrangements. On the other side, we introduce a wider class of hyperplane arrangements which is that of the symmetric hyperplane arrangements. Computing the Tutte polynomial of a symmetric hyperplane arrangement permits us to deduce the Tutte polynomials of some hyperplane arrangements, particularly of those associated to the imprimitive reflection groups.

Download Full-text

General position properties of ANR's

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100060163 ◽

1982 ◽

Vol 92 (3) ◽

pp. 451-466 ◽

Cited By ~ 1

Author(s):

W. J. R. Mitchell

Keyword(s):

Real Line ◽

General Position ◽

Cartesian Product ◽

Vital Role ◽

The Real ◽

Homology Groups ◽

Local Homology

This paper investigates the ‘general position’ properties which ANR's may possess. The most important of these is the disjoint discs property of Cannon (5), which plays a vital role in recent striking characterizations of manifolds (5, 9, 12, 18, 19, 22). Also considered are the property Δ of Borsuk(2) (which ensures an abundance of dimension-preserving maps), and the vanishing of local homology groups up to a given dimension (cf. (9)). Our main results give relations between these properties, and clarify their behaviour under the stabilization operation of taking cartesian product with the real line. In the last section these results are applied to give partial solutions to questions about homogeneous ANR's.

Download Full-text

Generalized Co-Cohen–Macaulay and Co-Buchsbaum Modules

Algebra Colloquium ◽

10.1142/s1005386707000260 ◽

2007 ◽

Vol 14 (02) ◽

pp. 265-278

Author(s):

Nguyen Tu Cuong ◽

Nguyen Thi Dung ◽

Le Thanh Nhan

Keyword(s):

Artinian Modules ◽

Basic Properties ◽

Local Homology

We study two classes of Artinian modules called co-Buchsbaum modules and generalized co-Cohen–Macaulay modules. Some basic properties and characterizations of these modules in terms of 𝔮-weak co-sequences, co-standard sequences, multiplicity, local homology modules are presented.

Download Full-text

Some properties of local homology and local cohomology modules

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/sscmath.50.2013.1.1233 ◽

2013 ◽

Vol 50 (1) ◽

pp. 129-141

Author(s):

Tran Nam

Keyword(s):

Local Cohomology ◽

Local Homology ◽

Local Cohomology Modules ◽

Cohomology Modules ◽

Compact Module

We study some properties of representable or I-stable local homology modules HiI (M) where M is a linearly compact module. By duality, we get some properties of good or at local cohomology modules HIi (M) of A. Grothendieck.

Download Full-text

Some results on local homology and local cohomology modules

Illinois Journal of Mathematics ◽

10.1215/ijm/1403534483 ◽

2013 ◽

Vol 57 (1) ◽

pp. 17-23 ◽

Cited By ~ 1

Author(s):

Shahram Rezaei

Keyword(s):

Local Cohomology ◽

Local Homology ◽

Local Cohomology Modules ◽

Cohomology Modules

Download Full-text

Orientations, Semiorders, Arrangements, and Parking Functions

The Electronic Journal of Combinatorics ◽

10.37236/2684 ◽

2012 ◽

Vol 19 (4) ◽

Cited By ~ 2

Author(s):

Sam Hopkins ◽

David Perkinson

Keyword(s):

Hyperplane Arrangement ◽

Parking Functions ◽

Its Regions

It is known that the Pak-Stanley labeling of the Shi hyperplane arrangement provides a bijection between the regions of the arrangement and parking functions. For any graph $G$, we define the $G$-semiorder arrangement and show that the Pak-Stanley labeling of its regions produces all $G$-parking functions.

Download Full-text