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                    MAT4540 - Algebraic Topology II
                  
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        <h1>Messages
          
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              <div class="vrtx-result-1 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/ny-eksamensplan.html">Ny eksamensplan</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Published              </span>
Jan. 15, 2026 11:06 AM            </div>


            <div class="description introduction">
                <p>Ny muntlig eksamen finner sted fredag 23. januar i rom B1120 (N. H. Abels hus), etter f?lgende tidsplan:</p><ul><li>11:15-12:00 ?smund S?ther</li></ul>
            </div>
        </div>



              <div class="vrtx-result-2 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/eksamensplan.html">Eksamensplan</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Published              </span>
Nov. 26, 2025 11:39 AM            </div>


            <div class="description introduction">
                <p>Muntlig eksamen finner sted fredag 5. desember i rom B1120 (N. H. Abels hus), etter f?lgende tidsplan:</p><ul><li>9:15-10:00 Anne Brug?rd</li><li>10:15-11:00 Edvard Walde Heimdal</li><li>11:15-12:00 Aksel L?vholt</li><li>13:15-14:00 Mattis Smaaland Nordgaard</li><li>14:15-15:00 ?smund S?ther</li></ul><p>?</p><p>?</p>
            </div>
        </div>



              <div class="vrtx-result-3 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/starting-question-for-oral-exam.html">Starting question for oral exam</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Published              </span>
Nov. 24, 2025 1:14 PM            </div>


            <div class="description introduction">
                <p>At the oral exam December 5th, each candidate will first be asked to "State and sketch a proof of the?Künneth formula of Theorem 3.15", taking up to a maximum of 10 minutes.</p>
            </div>
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              <div class="vrtx-result-4 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/syllabus.html">Syllabus</a>
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Published              </span>
Nov. 19, 2025 2:30 PM            </div>


            <div class="description introduction">
                <p>Page numbers refer to <a href="/studier/emner/matnat/math/MAT4540/h25/at.pdf">this version of Hatcher's book</a>.</p><p>Chapter 0</p><ul><li>Smash product (p. 10),</li><li>mapping cylinder and mapping cone (p. 13),</li><li>homotopy extension property (p. 14) and</li><li>Proposition 0.17.</li></ul><p>Chapter 3</p><ul><li>Pages <strong>190-204</strong>,</li><li><strong>206-223</strong> and</li><li><strong>230-254</strong> (omit details of proof of Lemma 3.36).</li></ul><p>Chapter 4</p><ul><li>Pages <strong>340-357</strong> (omit details of proof of Lemma 4.10;</li><li>only consider n-connected CW-models for (X, A) in the case of Postnikov sections and Whitehead covers;</li><li>omit proof of Proposition 4.21),</li><li><strong>360-367</strong>,</li><li>Hurewicz map (p. 370),</li><li><strong>375-378</strong>,</li><li><strong>393-399</strong> (omit proofs) and</li><li><strong>407-409</strong>.</li></ul>
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              <div class="vrtx-result-5 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/notes-on-homotopy-(co-)fibers-and-the-puppe-sequences.html">Notes on homotopy (co-)fibers and the Puppe sequences</a>
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Published              </span>
Oct. 31, 2025 3:20 PM            </div>


            <div class="description introduction">
                <p>Here are some<a href="/studier/emner/matnat/math/MAT4540/h25/puppe.pdf"> typed notes from my lectures</a> October 27th and 30th.</p>

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              <div class="vrtx-result-6 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/phdobligpresentasjon.html">PhDobligpresentasjon</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Published              </span>
Oct. 20, 2025 4:31 PM            </div>


            <div class="description introduction">
                <p>Som sin obligatoriske oppgave gir Anne Brug?rd en presentasjon om <a href="/studier/emner/matnat/math/MAT4540/h25/pres-a.pdf">kjedehomotopiekvivalenser og kvasiisomorfier</a> torsdag 23. oktober.</p>

            </div>
        </div>



              <div class="vrtx-result-7 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/mandatory-assignment.html">Obligatorisk oppgave</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Published              </span>
Sep. 29, 2025 1:08 PM            </div>


            <div class="description introduction">
                <p>Oppdatert 13. oktober:</p><p>Den obligatoriske oppgaven for master-studenter er n? tilgjengelig, i <a href="/studier/emner/matnat/math/MAT4540/h25/oblig.pdf">PDF</a>- og <a href="/studier/emner/matnat/math/MAT4540/h25/oblig.tex">LaTeX</a>-format.? Innleveringsfristen er torsdag 6. november kl. 23:59.? Gj?r innleveringen p? UiOs <a href="https://uio.instructure.com/courses/58406/assignments/129857">Canvas-side</a>.? Hint: Oppgavene 1, 5, 7 and 10 krever nok minst arbeid, dersom du forst?r hva som bes bevist i de mellomliggende oppgavene.? Detaljene i oppgave 9 er omfattende.</p><p>Tillegg 11. november:</p><p>De obligatoriske oppgavene er n? rettet, godkjent og innmeldt til studieinfo@math.uio.no.</p>
            </div>
        </div>



              <div class="vrtx-result-8 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/proposed-exam-date.html">Proposed exam date</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Published              </span>
Sep. 22, 2025 4:34 PM            </div>


            <div class="description introduction">
                <p>The current plan is to have the final (oral, not written) exam on Friday December 5th.&nbsp; Please write to rognes@math.uio.no if this does not work for you.</p>

<p>Added September 23rd: Room B1120 is now reserved for this exam, from 09:00 to 17:00 on December 5th.&nbsp; Each individual exam will last 45-60 minutes, according to a schedule to be determined in late November.</p>

            </div>
        </div>



              <div class="vrtx-result-9 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/note-on-cup-product-for-lecture-september-8th.html">Note on cup product for lecture September 8th</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Published              </span>
Sep. 7, 2025 8:52 PM            </div>


            <div class="description introduction">
                <p>Here are some <a href="/studier/emner/matnat/math/MAT4540/h25/cup.pdf">notes with simplified&nbsp;forms of Hatcher's Examples 3.7 and 3.8</a>.</p>

<p>&nbsp;</p>

            </div>
        </div>



              <div class="vrtx-result-10 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/notes-on-uct-for-lecture-august-21st..html">Notes on UCT for lectures August 21st, 25th and 28th.</a>
          </div>

            <div class="published-date">
              <span class="published-date-prefix">
Published              </span>
Aug. 20, 2025 3:06 PM            </div>


            <div class="description introduction">
                <p>I will use these <a href="/studier/emner/matnat/math/MAT4540/h25/uct.pdf">notes on chain complexes, the universal coefficient theorem and homological algebra</a> for the lectures on August 21st, 25th and 28th.&nbsp; (Last updated August 28th.)</p>

<p>&nbsp;</p>

            </div>
        </div>



              <div class="vrtx-result-11 vrtx-resource">
          <div class="vrtx-title">
            <a class="vrtx-title" href="/studier/emner/matnat/math/MAT4540/h25/beskjeder/initial-lectures.html">Initial lectures</a>
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            <div class="published-date">
              <span class="published-date-prefix">
Published              </span>
Aug. 11, 2025 12:39 PM            </div>


            <div class="description introduction">
                <p>I will start with a rough overview of the course, and then start on chapter 3 in <a href="https://pi.math.cornell.edu/~hatcher/AT/ATpage.html">Hatcher's textbook</a>.? We should discuss plans for weekly exercises and the mandatory assignment.? The course schedule will eventually contain a detailed plan of the course.? (If given the option, select "List" in place of "Calendar" for a more coherent overview.)</p>
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