A remark on the genus of the infinite quaternionic projective space

Maps to spaces in the genus of infinite quaternionic projective space

Spaces in the genus of infinite quaternionic projective space which admit essential maps from infinite complex projective space are classified. In these cases the sets of homotopy classes of maps are described explicitly. These results strengthen the classical theorem of McGibbon and Rector on maximal torus admissibility for spaces in the genus of infinite quaternionic projective space. An interpretation of these results in the context of Adams-Wilkerson embedding in integral $K$-theory is also given.

关于模2椭圆亏格的注记

Remarks on mod-2 elliptic genus

本文研究了模2椭圆亏格在超对称量子场论及拓扑模形式同态中的刻画，证明其在N=(0,1)超对称下由积分模形式的模2约化决定。

Toric genera of homogeneous spaces and their fibrations

The aim of this paper is to study further the universal toric genus of compact homogeneous spaces and their homogeneous fibrations. We consider the homogeneous spaces with positive Euler characteristic. It is well known that such spaces carry many stable complex structures equivariant under the canonical action of the maximal torus $T^k$. As the torus action in this case has only isolated fixed points it is possible to effectively apply localization formula for the universal toric genus. Using this we prove that the famous topological results related to rigidity and multiplicativity of a Hirze…

关于曲面有限覆盖同调的一个注记

A remark on the homology of finite coverings of a surface

本文证明了亏格不小于3的可定向闭曲面的有限覆盖中，有理同调群可由特定简单闭曲线上的循环生成，从而肯定回答了Autumn Kent提出的相关问题。