# ON THE S1-EULER CHARACTERISTIC OF THE SPACE WITH A CIRCLE ACTION ii

• HAN, SNAG-EON (Dept. of Computer and Applied Mathematics, College of Natural Sciences, Honam University)
• Published : 2002.07.30

#### Abstract

The $S^1$-Eule characteristics of X is defined by $\bar{\chi}_{S^1}(X)\;{\in}\;HH_1(ZG)$, where G is the fundamental group of connected finite $S^1$-compact manifold or connected finite $S^1$-finite complex X and $HH_1$ is the first Hochsch ild homology group functor. The purpose of this paper is to find several cases which the $S^1$-Euler characteristic has a homotopic invariant.

#### Acknowledgement

Supported by : Korea Research Foundation

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