论文标题
单元切线束同源性的映射课程组的稳定扭曲的共同体学
Stable twisted cohomology of the mapping class groups in the unit tangent bundle homology
论文作者
论文摘要
我们计算了一个边界的稳定绘制的可定向表面组的稳定共同体学组，并具有由表面的单位切线束的同源性给出的扭曲系数。这种稳定的扭曲的共同体并非作为模块在具有恒定系数的稳定同胞代数上是免费的。实际上，它超出了扭曲的共同体学稳定性的传统框架的范围，因为这些扭曲系数定义了与映射类群相关的经典类别以研究同源稳定性，而不是逆向的函数。为了进行比较，我们还计算了稳定的共同体学组，该组在表面的单位切线束的第一个共同体中，该系数适合传统框架。
We compute the stable cohomology groups of the mapping class groups of compact orientable surfaces with one boundary, with twisted coefficients given by the homology of the unit tangent bundle of the surface. This stable twisted cohomology is not free as a module over the stable cohomology algebra with constant coefficients. In fact, it is out of the scope of the traditional framework for twisted cohomological stability, since these twisted coefficients define a covariant functor over the classical category associated to mapping class groups to study homological stability, rather than a contravariant one. For comparison, we also compute the stable cohomology group with coefficients in the first cohomology of the unit tangent bundle of the surface, which fits into the traditional framework.
