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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Generalized Casson invariants for $ {\rm SO}(3),\;{\rm U}(2),\;{\rm Spin}(4),$ and $ {\rm SO}(4)$

Author: Cynthia L. Curtis
Journal: Trans. Amer. Math. Soc. 343 (1994), 49-86
MSC: Primary 57N10; Secondary 57M05
MathSciNet review: 1207580
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Abstract: We investigate Casson-type invariants corresponding to the low-rank groups $ {\text{SO}}(3)$, $ {\text{SU}}(2) \times {S^1}$, $ {\text{U}}(2)$, $ {\text{Spin}}(4)$ and $ {\text{SO}}(4)$. The invariants are defined following an approach similar to those of K. Walker and S. Cappell, R. Lee, and E. Miller. We obtain a description for each of the invariants in terms of the $ {\text{SU}}(2)$-invariant. Thus, all of them may be calculated using formulae for the $ {\text{SU}}(2)$-invariant. In defining these invariants, we offer methods which should prove useful for studying the invariants for other non-simply-connected groups once the invariants for the simply-connected covering groups are known.

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Article copyright: © Copyright 1994 American Mathematical Society