论文标题
Orbifolds，Orbispaces和全球同义理论
Orbifolds, Orbispaces and Global Homotopy Theory
论文作者
论文摘要
给定一个Orbifold，我们构建了代表其稳定的全局同型类型的正交谱。现在，正交光谱代表了Orbifold共同体学理论，它们自动满足某些特性，作为添加性和Mayer-Vietoris序列的存在。此外，可以通过歧管$ m $的$ g $ equivariant共同体来确定全球商$ m/g $的价值。由正交谱系代表的Orbifold共同学理论的例子包括Borel和Bredon的同学理论以及Orbifold $ K $ - 理论。这也意味着这些共同体组独立于将Orbifold作为全球商Orbifold的呈现。
Given an orbifold, we construct an orthogonal spectrum representing its stable global homotopy type. Orthogonal spectra now represent orbifold cohomology theories which automatically satisfy certain properties as additivity and the existence of Mayer-Vietoris sequences. Moreover, the value at a global quotient orbifold $M/G$ can be identified with the $G$-equivariant cohomology of the manifold $M$. Examples of orbifold cohomology theories which are represented by an orthogonal spectrum include Borel and Bredon cohomology theories and orbifold $K$-theory. This also implies that these cohomology groups are independent of the presentation of an orbifold as a global quotient orbifold.
