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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Generalized Casson invariants for $\textrm {SO}(3),\;\textrm {U}(2),\;\textrm {Spin}(4),$ and $\textrm {SO}(4)$
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by Cynthia L. Curtis PDF
Trans. Amer. Math. Soc. 343 (1994), 49-86 Request permission

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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 343 (1994), 49-86
  • MSC: Primary 57N10; Secondary 57M05
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1207580-9
  • MathSciNet review: 1207580