Characterizing maximal varieties via Bredon cohomology

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-08-14 DOI:10.1016/j.topol.2025.109544

Pedro F. dos Santos , Carlos Florentino , Javier Orts

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引用次数: 0

Abstract

We obtain a characterization of Maximal and Galois-Maximal

C_{2}

-spaces (including real algebraic varieties) in terms of

RO (C_{2})

-graded cohomology with coefficients in the constant Mackey functor

{\underline{F}}_{2}

, using the structure theorem of Clover May. Other known characterizations, for instance in terms of equivariant Borel cohomology, are also rederived from this. For the particular case of a smooth projective real variety V, equivariant Poincaré duality is used to deduce further symmetry restrictions for the decomposition of the

RO (C_{2})

-graded cohomology of the complex locus

V (C)

given by the same structure theorem. We illustrate this result with some computations, including the

RO (C_{2})

-graded cohomology with

{\underline{F}}_{2}

coefficients of real K3 surfaces.

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用Bredon上同调刻画极大变异

利用Clover May的结构定理，我们得到了常数Mackey函子F_2中带有系数的RO(C2)-梯度上同调的极大和伽罗-极大C2-空间（包括实代数变体）的刻划。其他已知的特征，例如在等变Borel上同调方面，也从这重新推导出来。对于光滑射影实数V的特殊情况，利用等变poincar对偶性进一步推导出由相同结构定理给出的复轨迹V(C)的RO(C2)-梯度上同调分解的对称约束。我们用一些计算来说明这一结果，包括实际K3表面的RO（C2）梯度与F_2系数的上同调。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.