Elementary abelian 2-group actions

on flag manifolds and applications

Authors:
Goutam Mukherjee and Parameswaran Sankaran

Journal:
Proc. Amer. Math. Soc. **126** (1998), 595-606

MSC (1991):
Primary 57R75, 57R85

DOI:
https://doi.org/10.1090/S0002-9939-98-04133-1

MathSciNet review:
1423325

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the unoriented cobordism ring. Let and let denote the equivariant cobordism ring of smooth manifolds with smooth -actions having finite stationary points. In this paper we show that the unoriented cobordism class of the (real) flag manifold is in the subalgebra generated by , where , and . We obtain sufficient conditions for indecomposability of an element in . We also obtain a sufficient condition for algebraic independence of any set of elements in . Using our criteria, we construct many indecomposable elements in the kernel of the forgetful map in dimensions , for , and show that they generate a polynomial subalgebra of .

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Additional Information

**Goutam Mukherjee**

Affiliation:
Stat-Math Division, Indian Statistical Institute, 203 B. T. Road, Calcutta-700 035, India

Email:
goutam@isical.ernet.in

**Parameswaran Sankaran**

Affiliation:
SPIC Mathematical Institute, 92 G. N. Chetty Road, Madras-600 017, India

Email:
sankaran@smi.ernet.in

DOI:
https://doi.org/10.1090/S0002-9939-98-04133-1

Received by editor(s):
July 11, 1996

Communicated by:
Thomas Goodwillie

Article copyright:
© Copyright 1998
American Mathematical Society