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Quasi-elliptic cohomology is a variant of elliptic cohomology theories. It is the orbifold K-theory of a space of constant loops. For global quotient orbifolds, it can be expressed in terms of equivariant K-theories. Thus, the constructions…

Algebraic Topology · Mathematics 2018-08-27 Zhen Huan

Quasi-elliptic cohomology is a variant of Tate K-theory. It is the orbifold K-theory of a space of constant loops. For global quotient orbifolds, it can be expressed in terms of equivariant K-theories. In this paper we show how this theory…

Algebraic Topology · Mathematics 2018-05-16 Zhen Huan

Ginzburg, Kapranov and Vasserot conjectured the existence of equivariant elliptic cohomology theories. In this paper, to give a description of equivariant spectra of the theories, we study an intermediate theory, quasi-elliptic cohomology.…

Algebraic Topology · Mathematics 2018-05-16 Zhen Huan

This paper gives an introduction to the homotopy theory of quasi-categories. Weak equivalences between quasi-categories are characterized as maps which induce equivalences on a naturally defined system of groupoids. These groupoids…

Category Theory · Mathematics 2019-09-19 J. F. Jardine

We describe the $K$-ring of a quasi-toric manifold in terms of generators and relations. We apply our results to describe the $K$-ring of Bott-Samelson varieties.

Algebraic Geometry · Mathematics 2007-05-23 P. Sankaran , V. Uma

In this paper we construct orthogonal $G-$spectra up to a weak equivalence for the quasi-theory $QE_{n, G}^*(-)$ corresponding to certain cohomology theories $E$. The construction of the orthogonal $G-$spectrum for quasi-elliptic cohomology…

Algebraic Topology · Mathematics 2018-09-21 Zhen Huan

Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…

Functional Analysis · Mathematics 2020-10-20 Reza Dehghanizade , Seyed Mohamad Sadegh Modarres Mosadegh

In this paper we construct a twisted version of quasi-elliptic cohomology. This theory can be constructed as a K-theory of a loop space. After establishing basic properties of the theory, including restriction, change-of-group and induction…

Algebraic Topology · Mathematics 2025-11-27 Zhen Huan

We construct a family of quasimetric spaces in generalized potential theory containing $m$-subharmonic functions with finite $(p,m)$-energy. These quasimetric spaces will be viewed both in $\mathbb{C}^n$ and in compact K\"ahler manifolds,…

Complex Variables · Mathematics 2021-10-07 Per Ahag , Rafal Czyz

We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.

K-Theory and Homology · Mathematics 2013-08-21 Jeremiah Heller , Jens Hornbostel

In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…

Operator Algebras · Mathematics 2012-11-06 Piotr M. Sołtan

In this paper we construct twisted Real quasi-elliptic cohomology as the twisted KR-theory of loop groupoids. The theory systematically incorporates loop rotation and reflection. After establishing basic properties of the theory, we…

Algebraic Topology · Mathematics 2022-10-17 Zhen Huan , Matthew B. Young

The concept of quasi-partial b-metric-like spaces is being introduced and studied with the help of topology. Examples are also discussed to support the results. Some fixed point theorems are proved in the setting of quasi-partial…

General Topology · Mathematics 2018-12-04 Anuradha Gupta , Manu Rohilla

The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…

Group Theory · Mathematics 2023-12-29 S. V. Ludkowski

In this article, we introduce and investigate the concept of partial quasi-metric type space as a generalization of both partial quasi-metric and quasi-metric type spaces. We show that many important constructions studied in K\"unzi's…

General Topology · Mathematics 2019-03-18 Yaé Ulrich Gaba

We refine the construction of quasi-homomorphisms on mapping class groups. It is useful to know that there are unbounded quasi-homomorphisms which are bounded when restricted to particular subgroups since then one deduces that the mapping…

Group Theory · Mathematics 2007-05-23 Mladen Bestvina , Koji Fujiwara

This is a survey of a new type of relativistic space-time framework; the so-called quasi-metric framework. The basic geometric structure underlying quasi-metric relativity is quasi-metric space-time; this is defined as a 4-dimensional…

General Relativity and Quantum Cosmology · Physics 2024-03-20 Dag Østvang

It is shown how traditional development of theories of fluids based upon the concept of physical clustering can be adapted to an alternative local clustering definition. The alternative definition can preserve a detailed valence description…

Chemical Physics · Physics 2015-06-26 Lawrence R. Pratt , Randall A. LaViolette

It is an old conjecture, that finite $H$-spaces are homotopy equivalent to manifolds. Here we prove that this conjecture is true for loop spaces. Actually, we show that every quasi finite loop space is equivalent to a stably parallelizable…

Algebraic Topology · Mathematics 2007-05-23 N. Kitchloo , D. Notbohm

In this paper, we construct a new homology theory for semi-groups satisfying the self distributivity axiom or the idempotency axiom. Next, we consider the geometric realization corresponding to the homology theory. We continue with the…

Geometric Topology · Mathematics 2016-11-18 Sujoy Mukherjee
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