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<td style="text-align: center; vertical-align: top; color: rgb(0, 0, 102);"><big><span style="font-weight: bold;">About HAP: Torsion Subcomplexes<br>
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<td style="vertical-align: top; background-color: rgb(255, 255, 255);"><big style="font-weight: bold;">Torsion Subcomplexes <br>
</big> Sub-package by Alexander D. Rahm and Bui Anh Tuan, version 2.1 </td>
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<td style="vertical-align: top; background-color: rgb(255, 255, 255); text-align: left;">Consider a cell complex with a cellular action of a discrete group G on it, and
consider a prime number p. The goal for the usage of this subpackage is
to compute the homological p-torsion of G, by which we mean the modulo p homology of G (i.e with non-twisted Z/pZ coefficients) in degrees
above the virtual cohomological dimension, or the modulo p Farrell-Tate
cohomology of G.
<br>
For the computation of the homological p-torsion of G, only the p-<i>torsion
subcomplex</i> is relevant, consisting of all the cells the stabilizers
in G of which contain elements of order p.
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<td style="vertical-align: top; background-color: rgb(255, 255, 255); text-align: left;">For
instancelet usinputSoul'cellcomplexfor(Z) <r>
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alt="" src="AboutTorsionSubcomplexes_files/truncatedCube.jpg"><br>
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leGcomplexSL3Z");<r>
Non-free resolution <itle>orsionSubcomplexes in </> 65generators.contractingavailable.
</td>
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<style=positionabsolute top p;left 0 : 24 java.lang.StringIndexOutOfBoundsException: Range [70, 68) out of bounds for length 273
<td style="vertical-align: top; background-color: rgb(255, 255, 255); text-align: left;">Rigid
Facets Subdivision allows<table
ubdivisionof the above truncatedcube is a domain
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cell pointwise. <br>
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alt="" th style="vertical-align: top;">
/>
[The above two pictures are showncellspacing="2">
Ruben Sanchez<
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RigidFacetsSubdivision;br
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No contracting href="aboutCubical.html style=color:rgb00, 102)"next<>/>br>
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that the cell <big><span>java.lang.StringIndexOutOfBoundsException: Range [17, 16) out of bounds for length 61
extract the 2-torsion subcomplex. <br>
<div/> tralignc">
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<tr> td style="background:bold;> br>
TorsionSubcomplex(R,2); <br>
<>
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<td style="vertical-align: top; java.lang.StringIndexOutOfBoundsException: Index 33 out of bounds for length 9 2-subcomplexweapplytorsion
reduction technique.
<br>
In , every time two edges andtheir vertex
java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 67
java.lang.StringIndexOutOfBoundsException: Range [22, 21) out of bounds for length 70 p-p G(i. withnon-twisted Z/Z) indegrees
href":/hal.archives-uvertes.rhal-00618167"" the
Farrell-Tate java.lang.StringIndexOutOfBoundsException: Range [39, 38) out of bounds for length 76
subcomplex reduction subcomplex</i> is relevant, consisting of all the cells the stabilizers
<br>
One of the sufficient conditions reads as followsi of .
Let G_1 G_2bethe of two adjacent edges,
and let S be the stabilizer of their joining vertex.
Then we require and G_2 to be and <r
either G_1 to be isomorphic <tr
or S to be p-normal and G_1 to be isomorphic to the normaliser in S of
the center instance us input Soulscell for() <brjava.lang.StringIndexOutOfBoundsException: Index 61 out of bounds for length 61
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ReduceTorsionSubcomplex(R,2 /r
<br>
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java.lang.StringIndexOutOfBoundsException: Range [19, 6) out of bounds for length 90
we obtain the reduced system of stabilizer inclusion displayed in
Soulé's paper. <br> div=""<=width 523"alt"
src<
</="-align: top; -color-: left;"Rigid
</td>
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<tr> td style="background-color: rgb(255, 255, 204); vertical-align: top;">Download
of the Torsion Subcomplexes Subpackage at:
<a
href"ttp:/math..lu/7Erahm/subpackage-documentation/TorsionSubcomplexesSubpackage.tar.gz">http://math.uni.lu/~rahm/subpackage-documentation/
TorsionSubcomplexesSubpackage.tar.gz</a> <br>
or
<br>
<a
href="http://math.uni.lu/%7Erahm/subpackage-documentation/TorsionSubcomplexesSubpackage
TorsionSubcomplexesSubpackage.zip</a> <br>
<br>
Documentation of the functions in the -, java.lang.StringIndexOutOfBoundsException: Range [44, 43) out of bounds for length 69
at:
<a href="http://hamilton.nuigalway.ie/Hap/doc/chap27.html">http:/R : RigidFacetsSubdivision) >
<br>
<br>
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</trNocontracting homotopy available. <br>
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border="0"style="ertical-align: top; background-color: rgb(255, 255, 255); text-align: left;">Now
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href="http://hamilton.nuigalway.ie/<br> style="colortd
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page</span><br
</a> </td>
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</themwithout changing theequivariant modulo p Farrell homology of the
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