Beispiel #1
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 def testInvolutiveRankL31(self):
     "Check that the involutive Floer homology of L(3,1) is F_2^4."
     P = infTypeD(1)
     Q = infTypeD(1)
     R = ArcslideDA(Arcslide(splitPMC(1),1,0))
     Q2 = R.tensorD(Q)
     Q3 = R.tensorD(Q2)
     Q4 = R.tensorD(Q3)
     othcx = P.morToD(Q4)
     othcx.simplify()
     cx = involutiveCx(P,Q3)
     self.assertTrue(len(othcx)==3)
     self.assertTrue(len(cx)==4)
Beispiel #2
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 def testGrading(self):
     d1 = zeroTypeD(1)
     d2 = infTypeD(1)
     dd_id = identityDD(splitPMC(1))
     cx = computeATensorD(d1.dual(), d2)
     dstr1 = computeDATensorD(dd_id, d1)
     dstr2 = computeATensorDD(d1, dd_id)
Beispiel #3
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 def testDATensorD(self):
     dastr = identityDA(splitPMC(2))
     dstr = zeroTypeD(2)
     dstr_result = dastr.tensorD(dstr)
     cx = dstr_result.morToD(infTypeD(2))
     cx.simplify()
     # Basic check that dstr_result is still zeroTypeD(2)
     self.assertEqual(len(cx), 1)
Beispiel #4
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 def testMorToD(self):
     id2 = identityDD(splitPMC(2))
     d = infTypeD(2)
     d2 = id2.morToD(d)
     self.assertTrue(d2.testDelta())
     d2.simplify()
     self.assertEqual(len(d2), 1)
     d3 = zeroTypeD(2)
     d4 = id2.morToD(d3)
     self.assertTrue(d4.testDelta())
     d4.simplify()
     self.assertEqual(len(d4), 1)
Beispiel #5
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    def openCap(self):
        """Returns the type D structure corresponding to this handlebody by
        tensoring type DA bimodules with the genus-1 handlebody.

        """
        assert self.genus > 0
        last_move, prev_cap = self.getLastCobordism()
        if self.genus == 1:
            if last_move == 0:
                return zeroTypeD(1)
            else:
                return infTypeD(1)
        else:
            cur_da = CobordismDALeft(Cobordism(self.genus, last_move, LEFT))
            dstr = cur_da.tensorD(prev_cap.openCap())
            dstr.simplify()
            dstr.reindex()
        return dstr
Beispiel #6
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def platTypeD2(genus, is_dual = False):
    """Obtain linear handlebody from inf-framed handlebody by a sequence of
    arcslides. As the inf-framed handlebody has absolute grading, we can get
    absolute grading on this D structure.

    """
    start = infTypeD(genus, is_dual)
    slides = []
    for i in range(genus-1):
        slides += [(4*i+3,4*i+4), (4*i+6,4*i+7), (4*i+5,4*i+6)]
    cur_pmc = splitPMC(genus)
    for i in range(len(slides)):
        b1, c1 = slides[i]
        slides[i] = Arcslide(cur_pmc, b1, c1)
        cur_pmc = slides[i].end_pmc
    if not is_dual:
        slides = [slide.inverse() for slide in slides]
    slides_dd = [slide.getDDStructure() for slide in slides]
    return composeDD(start, slides_dd, is_dual)
Beispiel #7
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 def testInvolutiveRankS3(self):
     "Check that the involutive Floer homology of S^3 is F_2^2."
     P = zeroTypeD(1)
     Q = infTypeD(1)
     cx = involutiveCx(P,Q)
     self.assertTrue(len(cx)==2)