scholarly journals On the classification of rational homotopy types of elliptic spaces with homotopy Euler characteristic zero for dim < 8

2011 ◽  
Vol 18 (5) ◽  
pp. 925-939 ◽  
Author(s):  
Mamoru Mimuraz ◽  
Hiroo Shiga
Keyword(s):  
Euler Characteristic ◽  
Characteristic Zero ◽  
Rational Homotopy ◽  
Homotopy Types ◽  
Elliptic Spaces

scholarly journals Classification of rational homotopy type for 10-cohomological dimension elliptic spaces

Mathematica ◽  
2020 ◽  
Vol 62 (85) (1) ◽  
pp. 16-32
Author(s):  
Saloua Chouingou ◽  
◽  
Mohamed Rachid Hilali ◽  
Keyword(s):  
Homotopy Type ◽  
Cohomological Dimension ◽  
Rational Homotopy ◽  
Rational Homotopy Type ◽  
Elliptic Spaces

FIXED ELEMENTS OF NONINJECTIVE ENDOMORPHISMS OF POLYNOMIAL ALGEBRAS IN TWO VARIABLES

2016 ◽  
Vol 95 (2) ◽  
pp. 209-213
Author(s):  
YUEYUE LI ◽  
JIE-TAI YU
Keyword(s):  
Associative Algebra ◽  
Characteristic Zero ◽  
Polynomial Algebra ◽  
Free Associative Algebra ◽  
Polynomial Algebras ◽  
Fixed Element ◽  
The Given

Let $A_{2}$ be a free associative algebra or polynomial algebra of rank two over a field of characteristic zero. The main results of this paper are the classification of noninjective endomorphisms of $A_{2}$ and an algorithm to determine whether a given noninjective endomorphism of $A_{2}$ has a nontrivial fixed element for a polynomial algebra. The algorithm for a free associative algebra of rank two is valid whenever an element is given and the subalgebra generated by this element contains the image of the given noninjective endomorphism.

scholarly journals COMBINATORIAL AND TOPOLOGICAL PHASE STRUCTURE OF NON-PERTURBATIVE n-DIMENSIONAL QUANTUM GRAVITY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2109-2121
Author(s):  
M. CARFORA ◽  
M. MARTELLINI ◽  
A. MARZUOLI
Keyword(s):  
Quantum Gravity ◽  
Phase Structure ◽  
Gravity Models ◽  
Topological Phase ◽  
Geometrical Characterization ◽  
Homotopy Types ◽  
Geometrical Constraints ◽  
Riemannian Geometries

We provide a non-perturbative geometrical characterization of the partition function of ndimensional quantum gravity based on a rough classification of Riemannian geometries. We show that, under natural geometrical constraints, the theory admits a continuum limit with a non-trivial phase structure parametrized by the homotopy types of the class of manifolds considered. The results obtained qualitatively coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.

Applications of Decomposition Theorems to Trivializing h-Cobordisms

1977 ◽  
Vol 20 (3) ◽  
pp. 389-391 ◽  
Author(s):  
Terry Lawson
Keyword(s):  
Euler Characteristic ◽  
Characteristic Zero ◽  
Closed Manifold ◽  
Geometric Proof ◽  
Open Book ◽  
Open Book Decompositions ◽  
Decomposition Theorems

AbstractA geometric proof is presented that, under certain restrictions, the product of an h-cobordism with a closed manifold of Euler characteristic zero is a product cobordism. The results utilize open book decompositions and round handle decompositions of manifolds.

scholarly journals Algebraic Surfaces of General Type with Small c21 in Positive Characteristic

2008 ◽  
Vol 191 ◽  
pp. 111-134 ◽  
Author(s):  
Christian Liedtke
Keyword(s):  
Characteristic Zero ◽  
General Type ◽  
Positive Characteristic ◽  
Algebraic Surfaces ◽  
Surfaces Of General Type ◽  
Arbitrary Characteristic ◽  
Numerical Invariants ◽  
Characteristic 2

AbstractWe establish Noether’s inequality for surfaces of general type in positive characteristic. Then we extend Enriques’ and Horikawa’s classification of surfaces on the Noether line, the so-called Horikawa surfaces. We construct examples for all possible numerical invariants and in arbitrary characteristic, where we need foliations and deformation techniques to handle characteristic 2. Finally, we show that Horikawa surfaces lift to characteristic zero.

scholarly journals Classification of stable homotopy types with torsion-free homology

Topology ◽  
2001 ◽  
Vol 40 (4) ◽  
pp. 789-821 ◽  
Author(s):  
Hans-Joachim Baues ◽  
Yuri Drozd
Keyword(s):  
Stable Homotopy ◽  
Homotopy Types ◽  
Torsion Free

scholarly journals MOTIVIC EULER CHARACTERISTICS AND WITT-VALUED CHARACTERISTIC CLASSES

2019 ◽  
Vol 236 ◽  
pp. 251-310 ◽  
Author(s):  
MARC LEVINE
Keyword(s):  
Euler Characteristic ◽  
Characteristic Zero ◽  
Maximal Torus ◽  
Vector Bundles ◽  
Reductive Group ◽  
Characteristic Classes ◽  
Euler Characteristics ◽  
Symmetric Powers ◽  
Maximal Tori ◽  
General Calculus

This paper examines Euler characteristics and characteristic classes in the motivic setting. We establish a motivic version of the Becker–Gottlieb transfer, generalizing a construction of Hoyois. Making calculations of the Euler characteristic of the scheme of maximal tori in a reductive group, we prove a generalized splitting principle for the reduction from $\operatorname{GL}_{n}$ or $\operatorname{SL}_{n}$ to the normalizer of a maximal torus (in characteristic zero). Ananyevskiy’s splitting principle reduces questions about characteristic classes of vector bundles in $\operatorname{SL}$-oriented, $\unicode[STIX]{x1D702}$-invertible theories to the case of rank two bundles. We refine the torus-normalizer splitting principle for $\operatorname{SL}_{2}$ to help compute the characteristic classes in Witt cohomology of symmetric powers of a rank two bundle, and then generalize this to develop a general calculus of characteristic classes with values in Witt cohomology.

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