Abstract
In the present paper, we discuss an obstruction theory to modify equivariant framed maps on even-dimensional compact smooth manifolds to homology equivalences by equivariant surgery. In 1974, Cappell-Shaneson already developed such obstruction theory in the nonequivariant setting. Our definition of the surgery-obstruction group presents a new aspect of Cappell-Shaneson's group in the nonequivariant setting and enables us to define directly the surgery obstructions of certain framed maps that are not necessarily connected up to the middle dimension. Using our framework defining the equivariant surgery obstruction, we prove a basic conjecture related to geometric connected sums and algebraic sums of surgery obstructions.
| Original language | English |
|---|---|
| Pages (from-to) | 481-506 |
| Number of pages | 26 |
| Journal | Publications of the Research Institute for Mathematical Sciences |
| Volume | 42 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - Jun 2006 |
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Keywords
- Equivariant surgery
- Gap condition
- Homology equivalence
- Surgery obstruction
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Equivariant surgery theory for homology equivalences under the gap condition. / Morimoto, Masaharu.
In: Publications of the Research Institute for Mathematical Sciences, Vol. 42, No. 2, 06.2006, p. 481-506.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Equivariant surgery theory for homology equivalences under the gap condition
AU - Morimoto, Masaharu
PY - 2006/6
Y1 - 2006/6
N2 - In the present paper, we discuss an obstruction theory to modify equivariant framed maps on even-dimensional compact smooth manifolds to homology equivalences by equivariant surgery. In 1974, Cappell-Shaneson already developed such obstruction theory in the nonequivariant setting. Our definition of the surgery-obstruction group presents a new aspect of Cappell-Shaneson's group in the nonequivariant setting and enables us to define directly the surgery obstructions of certain framed maps that are not necessarily connected up to the middle dimension. Using our framework defining the equivariant surgery obstruction, we prove a basic conjecture related to geometric connected sums and algebraic sums of surgery obstructions.
AB - In the present paper, we discuss an obstruction theory to modify equivariant framed maps on even-dimensional compact smooth manifolds to homology equivalences by equivariant surgery. In 1974, Cappell-Shaneson already developed such obstruction theory in the nonequivariant setting. Our definition of the surgery-obstruction group presents a new aspect of Cappell-Shaneson's group in the nonequivariant setting and enables us to define directly the surgery obstructions of certain framed maps that are not necessarily connected up to the middle dimension. Using our framework defining the equivariant surgery obstruction, we prove a basic conjecture related to geometric connected sums and algebraic sums of surgery obstructions.
KW - Equivariant surgery
KW - Gap condition
KW - Homology equivalence
KW - Surgery obstruction
UR - http://www.scopus.com/inward/record.url?scp=33747634745&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33747634745&partnerID=8YFLogxK
U2 - 10.2977/prims/1166642112
DO - 10.2977/prims/1166642112
M3 - Article
AN - SCOPUS:33747634745
VL - 42
SP - 481
EP - 506
JO - Publications of the Research Institute for Mathematical Sciences
JF - Publications of the Research Institute for Mathematical Sciences
SN - 0034-5318
IS - 2
ER -