旗流形与Landweber-Novikov代数
Flag manifolds and the Landweber-Novikov algebra
摘要：
研究了Landweber-Novikov代数S^* 及其积分对偶S_* 的各种结构映射的几何解释。特别地，我们研究了S_* 中的余积和对极，以及S^* 在S_* 上的左作用和右作用，它们是量子（或Drinfeld）二重D（S^*）的构造基础。我们设置我们的实现的背景下，二重复形的配边，利用某些流形的有界旗，推广复射影空间，并可能被正则表示为环面品种。我们讨论了他们的细胞结构类比与经典的舒伯特分解，并详细说明了庞加莱对偶的影响与双协边理论，这些直接导致我们的主要结果Landweber-Novikov代数。
英文摘要：
We investigate geometrical interpretations of various structure maps associated with the Landweber-Novikov algebra S^* and its integral dual S_*. In particular, we study the coproduct and antipode in S_*, together with the left and right actions of S^* on S_* which underly the construction of the quantum (or Drinfeld) double D(S^*). We set our realizations in the context of double complex cobordism, utilizing certain manifolds of bounded flags which generalize complex projective space and may be canonically expressed as toric varieties. We discuss their cell structure by analogy with the classical Schubert decomposition, and detail the implications for Poincare duality with respect to double cobordism theory; these lead directly to our main results for the Landweber-Novikov algebra.
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