# Splitting obstructions and properties of objects in the Nil categories

Fundamenta Mathematicae (1999)

- Volume: 161, Issue: 1-2, page 155-165
- ISSN: 0016-2736

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topKoźniewski, Tadeusz. "Splitting obstructions and properties of objects in the Nil categories." Fundamenta Mathematicae 161.1-2 (1999): 155-165. <http://eudml.org/doc/212397>.

@article{Koźniewski1999,

abstract = {We show that the objects of Bass-Farrell categories which represent 0 in the corresponding Nil groups are precisely those which are stably triangular. This extends to Waldhausen's Nil group of the amalgamated free product with index 2 factors. Applications include a description of Cappell's special UNil group and reformulations of those splitting and fibering theorems which use the Nil groups.},

author = {Koźniewski, Tadeusz},

journal = {Fundamenta Mathematicae},

keywords = {triangular object; Bass-Farrell categories; Nil-groups; -groups; -groups; splitting; fibering},

language = {eng},

number = {1-2},

pages = {155-165},

title = {Splitting obstructions and properties of objects in the Nil categories},

url = {http://eudml.org/doc/212397},

volume = {161},

year = {1999},

}

TY - JOUR

AU - Koźniewski, Tadeusz

TI - Splitting obstructions and properties of objects in the Nil categories

JO - Fundamenta Mathematicae

PY - 1999

VL - 161

IS - 1-2

SP - 155

EP - 165

AB - We show that the objects of Bass-Farrell categories which represent 0 in the corresponding Nil groups are precisely those which are stably triangular. This extends to Waldhausen's Nil group of the amalgamated free product with index 2 factors. Applications include a description of Cappell's special UNil group and reformulations of those splitting and fibering theorems which use the Nil groups.

LA - eng

KW - triangular object; Bass-Farrell categories; Nil-groups; -groups; -groups; splitting; fibering

UR - http://eudml.org/doc/212397

ER -

## References

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- [FH1] F. T. Farrell and W. C. Hsiang, A formula for ${K}_{1}{R}_{\alpha}\left[T\right]$, in: Proc. Sympos. Pure Math. 17, Amer. Math. Soc., 1970, 192-218.
- [FH2] F. T. Farrell and W. C. Hsiang, Manifolds with ${\pi}_{1}=G{\times}_{\alpha}T$, Amer. J. Math. 95 (1973), 813-848.
- [KS] S. Kwasik and R. Schultz, Unitary nilpotent groups and the stability of pseudoisotopies, Duke Math. J. 71 (1993), 871-887. Zbl0804.57009
- [R] A. Ranicki, Lower K- and L-Theory, Cambridge Univ. Press, 1992.
- [W1] F. Waldhausen, Whitehead groups of generalized free products, preprint, 1969.
- [W2] F. Waldhausen, Algebraic K-theory of generalized free products, Ann. of Math. 108 (1978), 135-256. Zbl0407.18009

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