Multiplicative structure of the cohomology ring of real toric spaces

2020 ◽  
Vol 22 (1) ◽  
pp. 97-115
Author(s):  
Suyoung Choi ◽  
Hanchul Park
Keyword(s):  
Cohomology Ring ◽  
Multiplicative Structure

scholarly journals COHOMOLOGY RING OF THE BRST OPERATOR ASSOCIATED TO THE SUM OF TWO PURE SPINORS

2013 ◽  
Vol 28 (23) ◽  
pp. 1350107 ◽  
Author(s):  
ANDREI MIKHAILOV ◽  
ALBERT SCHWARZ ◽  
RENJUN XU
Keyword(s):  
Cohomology Ring ◽  
Type Ii ◽  
Pure Spinor ◽  
Multiplicative Structure ◽  
Dimensional Algebra ◽  
Dimensional Vector Space ◽  
Infinite Dimensional ◽  
Brst Operator ◽  
Finite Dimensional ◽  
Algebra Of Functions

In the study of the Type II superstring, it is useful to consider the BRST complex associated to the sum of two pure spinors. The cohomology of this complex is an infinite-dimensional vector space. It is also a finite-dimensional algebra over the algebra of functions of a single pure spinor. In this paper we study the multiplicative structure.

scholarly journals The cohomology ring of the sapphires that admit the Sol geometry

2018 ◽  
Vol 28 (03) ◽  
pp. 365-380 ◽  
Author(s):  
Daciberg Lima Gonçalves ◽  
Sérgio Tadao Martins
Keyword(s):  
Fundamental Group ◽  
Cohomology Ring ◽  
Free Resolution ◽  
Multiplicative Structure ◽  
Torus Bundle ◽  
Cohomology Rings ◽  
Cup Product ◽  
Diagonal Approximation

Let [Formula: see text] be the fundamental group of a sapphire that admits the Sol geometry and is not a torus bundle. We determine a finite free resolution of [Formula: see text] over [Formula: see text] and calculate a partial diagonal approximation for this resolution. We also compute the cohomology rings [Formula: see text] for [Formula: see text] and [Formula: see text] for an odd prime [Formula: see text], and indicate how to compute the groups [Formula: see text] and the multiplicative structure given by the cup product for any system of coefficients [Formula: see text].

A Generalization of “Concordance of PL-Homeomorphisms of Sp × Sq

1972 ◽  
Vol 24 (3) ◽  
pp. 426-431 ◽  
Author(s):  
J. P. E. Hodgson
Keyword(s):  
Equivalence Relation ◽  
Cohomology Ring

Let Mm be a closed PL manifold of dimension m. Then a concordance between two PL-homeomorphisms h0, h1:M → M is a PL-homeomorphismH: M × I → M × I such that H|M × 0 = h0 and H|M × 1 = h. Concordance is an equivalence relation and in his paper [2], M. Kato classifies PL-homeomorphisms of Sp × Sq up to concordance. To do this he treats first the problem of classifying those homeomorphisms that induce the identity in homology, and then describes the automorphisms of the cohomology ring that can arise from homeomorphisms of Sp × Sq. In this paper we show that for sufficiently connected PL-manifolds that embed in codimension 1, one can extend Kato's classification of the homeomorphisms that induce the identity in homology.

scholarly journals The existence of generating families for the cohomology ring of a graph

2003 ◽  
Vol 174 (1) ◽  
pp. 115-153 ◽  
Author(s):  
Victor Guillemin ◽  
Catalin Zara
Keyword(s):  
Cohomology Ring

The polynomial cohomology ring for characteristicp

1962 ◽  
Vol 79 (1) ◽  
pp. 297-306
Author(s):  
Robert Heaton
Keyword(s):  
Cohomology Ring

scholarly journals Cohomology of groups and splendid equivalences of derived categories

2001 ◽  
Vol 131 (3) ◽  
pp. 459-472 ◽  
Author(s):  
ALEXANDER ZIMMERMANN
Keyword(s):  
Group Ring ◽  
Local Structure ◽  
Cohomology Ring ◽  
Derived Categories ◽  
Derived Category ◽  
Restriction Map ◽  
Group Rings ◽  
Cohomology Rings ◽  
The Impact ◽  
Cohomology Of Groups

In an earlier paper we studied the impact of equivalences between derived categories of group rings on their cohomology rings. Especially the group of auto-equivalences TrPic(RG) of the derived category of a group ring RG as introduced by Raphaël Rouquier and the author defines an action on the cohomology ring of this group. We study this action with respect to the restriction map, transfer, conjugation and the local structure of the group G.

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