不动点集为 CP(2ⁿ)×HP(2^m+1) 的对合

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中图分类号：O189.3 文献标识码：A DOI：10.7535/hbkd.2026yx02007

Abstract：Inordertodevelop equivariantcobordismclasificationof manifoldswith involutions whose fixedpoint setsare product of projective spaces，the equivariant cobordism classification of all manifolds with involutions （M，T） with fixed point set F=CP（2n）×HP（2m+1）（m≥n⩾3） was studied. Firstly，the existence of bounding involutions with CP 1 （2n）× （204号 HP 1 （2m+1） as its fixed point set was proved; Secondly，according to the form of normal bundle over F ，the results were discussedbydividing several cases，byconstructing a suitable symmetric polynomial，according to Kosniowski-Stong theorem， thecontradiction wasobtainedbycalculating characteristicnumbers，and non-existenceofnon-bounding involutionswas proved，or that involutions exist andbordism wasobtainedbycalculating characteristic numbers；Finall，bordism was obtained. The results show that every smooth closed manifold （M，T） with an involution T having fixed point set of form CP（2n）×HP（2m+1）（m≥n≥3） ）exists and bounds. The research results enrich the equivariant cobordism classification of involutionswith fixedpoint setproductof projectivespaces，andprovidetheoretical reference for thefurther study involutions with fixed point set other special manifold.

Keywords： algebraic topology； involution; fixed point set；characteristic class；cobordism class

设 M 是一个未定向的光滑闭流形， T：MM 为 M 上的光滑对合，对合的不动点集为 F={x∈M} T（x）=x} 。（剩余8950字）