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Transactions of the American Mathematical Society

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



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

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