Geodesic
Bitwist 3–manifolds
Cannon, James W1 ; Floyd, William J2 ; Parry, Walter R3
1Department of Mathematics, Brigham Young University, Provo, UT 84602, USA
2Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
3Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA
Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 187-220
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Our earlier twisted-face-pairing construction showed how to modify an arbitrary orientation-reversing face-pairing on a faceted 3–ball in a mechanical way so that the quotient is automatically a closed, orientable 3–manifold. The modifications were, in fact, parametrized by a finite set of positive integers, arbitrarily chosen, one integer for each edge class of the original face-pairing. This allowed us to find very simple face-pairing descriptions of many, though presumably not all, 3–manifolds.

Here we show how to modify the construction to allow negative parameters, as well as positive parameters, in the twisted-face-pairing construction. We call the modified construction the bitwist construction. We prove that all closed connected orientable 3–manifolds are bitwist manifolds. As with the twist construction, we analyze and describe the Heegaard splitting naturally associated with a bitwist description of a manifold.

DOI : 10.2140/agt.2009.9.187
Keywords: 3–manifold constructions, Dehn surgeries

Cannon, James W  1   ; Floyd, William J  2   ; Parry, Walter R  3

1 Department of Mathematics, Brigham Young University, Provo, UT 84602, USA
2 Department of Mathematics, Virginia Tech, Blacksburg, VA 24061, USA
3 Department of Mathematics, Eastern Michigan University, Ypsilanti, MI 48197, USA 
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Cannon, James W; Floyd, William J; Parry, Walter R. Bitwist 3–manifolds. Algebraic and Geometric Topology, Tome 9 (2009) no. 1, pp. 187-220. doi: 10.2140/agt.2009.9.187

[1] R J Ackermann, Constructing bitwisted face pairing 3–manifolds, MS thesis, Virginia Tech (2008)

[2] J W Cannon, W J Floyd, W R Parry, Introduction to twisted face-pairings, Math. Res. Lett. 7 (2000) 477

[3] J W Cannon, W J Floyd, W R Parry, Twisted face-pairing 3–manifolds, Trans. Amer. Math. Soc. 354 (2002) 2369

[4] J W Cannon, W J Floyd, W R Parry, Heegaard diagrams and surgery descriptions for twisted face-pairing 3–manifolds, Algebr. Geom. Topol. 3 (2003) 235

[5] N M Dunfield, W P Thurston, Finite covers of random 3–manifolds, Invent. Math. 166 (2006) 457

[6] R E Gompf, A I Stipsicz, 4–manifolds and Kirby calculus, Graduate Studies in Mathematics 20, American Mathematical Society (1999)

[7] A Kawauchi, A survey of knot theory, Birkhäuser Verlag (1996)

[8] R L Moore, Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27 (1925) 416

[9] V V Prasolov, A B Sossinsky, Knots, links, braids and 3–manifolds, Translations of Mathematical Monographs 154, American Mathematical Society (1997)

[10] D Rolfsen, Knots and links, Mathematics Lecture Series 7, Publish or Perish (1976)

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