论文标题
Orbifold Bordism和二元性，用于有限的Orbispectra
Orbifold bordism and duality for finite orbispectra
论文作者
论文摘要
我们构建了有限orbispectra的稳定（代表性）同拷贝类别，其对象是通过矢量束的有限orbi-cw对的形式分解，其形态是稳定的（代表）相对图的稳定同型类别。有限的Orbispectra的稳定代表同型类别承认，违反的相互作用扩展了士兵 - 白头双重性。这种二元性与由全球thom光谱代表的同型恢复理论（有限的Orbispectra）相关的同位学理论（共同体理论）与Orbifold Bordism组（有限的Orbispectra的同源理论）表示。这种同构延伸了经典的蓬松素 - 滋养及其已知的术概括。
We construct the stable (representable) homotopy category of finite orbispectra, whose objects are formal desuspensions of finite orbi-CW-pairs by vector bundles and whose morphisms are stable homotopy classes of (representable) relative maps. The stable representable homotopy category of finite orbispectra admits a contravariant involution extending Spanier--Whitehead duality. This duality relates homotopical cobordism theories (cohomology theories on finite orbispectra) represented by global Thom spectra to geometric (derived) orbifold bordism groups (homology theories on finite orbispectra). This isomorphism extends the classical Pontryagin--Thom isomorphism and its known equivariant generalizations.
